Migration and Economic Recovery During COVID-19¶

Executive Summary¶

My project will analyze migration patterns and economic recovery following the COVID-19 pandemic to understand the potential relationship between the two and attempt to predict future migration trends.

The ability to predict which areas of the US will grow in population faster than others after a national crisis is especially relevant to policymakers, who must prioritize government aid to the areas that need it most. During COVID, there were billions of dollars of federal money given to states and cities to help them recover from the pandemic, leaving local policymakers to make decisions about where to best allocate this spending.[1] While COVID-19 may seem like a rare scenario, a recent study by the Proceedings of the National Academy of Sciences warns that similar pandemics will become more common in the future.[2] If policymakers are able to predict migration flows at a county-level, they will have a better sense of how to allocate aid on a per capita basis that reflects where people will be located in the future. Aid may also be more useful in areas that will continue to lose a lot of their population, which will inevitably affect the local economy. Furthermore, if these trends hold in post-COVID settings, predicting regional population growth could prove useful for other, non-crisis government initiatives, like infrastructure projects.

To accomplish these tasks, I employ county-level economic data that measure the impact of the COVID-19 pandemic on consumer spending, employment, and small businesses. Additionally, I use data on post office change of address requests to estimate migration patterns at the county-level. The result of this project is a model that can predict migration patterns, primarily through seasonal trends, but with slightly increased accuracy using economic data. I find that there are strong correlations between economic activity and migration patterns, though these relationships only lead to modest improvements in a model that attempts to predict future migration patterns.

Problem Statement¶

The COVID-19 pandemic caused an unprecedented economic shutdown across the United States, weakening the economy and closing businesses for months.[3] Simultaneously, the rise of remote work enabled workers to move further away from their office location without penalty. Previous work on this subject has found that during the pandemic, people moved away from central cities and into surrounding suburbs.[4] This raises the question of whether areas with greater migration inflow are also places that experienced less economic damage during 2020, as people were possibly drawn to areas due to the lower COVID impact on the local economy. If so, we may be able to use this same data to predict migration trends in the short-run, especially now that many workers are no longer confined to living near their company headquarters and can more easily relocate to more prosperous areas.

This project paints a picture of migration and economic recovery during COVID across the United States and uses this data to predict migration trends post-COVID. In the modern day, we have large amounts of data on economic activity that can be accessed quickly and used during crises to inform policy decisions. Knowing which variables are most useful in predicting future migration trends will be essential in responding quickly to these crises. Additionally, if we can leverage economic and migration data to predict future trends, this can be another tool for policymakers when designing more standard economic policies.

For this project, I use data from two sources. First, I gather data from Opportunity Insights.[5] Opportunity Insights is a group of researchers that uses economic data to explore inequalities across the United States. During COVID-19, this group partnered with several companies to track how the pandemic had affected local economies in the US and subsequently track the local recovery as the pandemic progressed. Specifically, they have data on county-level credit/debit card spending, employment, small business revenues and openings, and cellphone mobility. Second, I gather migration data from the United States Postal Service (USPS).[6] USPS collects data on monthly address changes at the ZIP code level. For each month, they report the total address changes into a ZIP code and the total address changes out of a ZIP code, allowing me to approxmiate how many people are moving to and away from each ZIP code.

The speed at which this data can be collected and processed is extremely powerful. For example, Opportunity Insights posts data on daily credit/debit card spending at the county-level within a few weeks of the activity. Additionally, monthly USPS data becomes available soon after the month ends, meaning we can use very recent data on economic activity and migration to predict future trends. One of the goals of this project, therefore, is to explore the potential of this data to make predictions in the near future, which will hopefully make those predictions more accurate.

Using these data sources and with the above motivation, this analysis sets out to answer the following questions:

  1. What is the correlation between population movement, as tracked through USPS, and economic indicators? Did areas that saw increased migration post-COVID also experience less economic damage?
  2. Which variables in these data are the strongest predictors of migration?
  3. Can we use a combination of migration and economic data to project migration patterns in the short-term?
  4. Which model is best for predicting migration patterns at the county-level?

To achieve these results, I use a combination of exploratory analysis, hypothesis testing, ordinary least squares regressions, L1/L2 regularization, and STL decomposition techniques.

Based on the initial exploratory data analysis, there appear to be correlations between migration to an area and that area's economic recovery, though there is substantial variation by state. This is expected, given differences between states in lockdown severity and length during the onset of COVID-19. The relationships between economic variables and migration also appear to vary over time in some cases, with correlations strengthening or weakening as the years progress. More formal OLS regressions show negative correlations between migration and consumer spending, employment, and small business revenue. These regressions also show a positive correlation between migration and foot traffic to retail and recreation businesses.

With these insights in mind, I remove the seasonal and trend components of the migration data and use the lagged economic variables to predict the remaining residuals of the migration data. I test several models and find that the optimal model uses all of the economic variables, without county fixed-effects. Using economic variables only presents modest gains in accuracy, as most of the population changes can be modeled with the seasonal variation.

Data Construction¶

This section of code walks through the various datasets and how they are aggregated and merged to form my full dataset.

In [1]:
import pandas as pd
import numpy as np
import numpy.random as nr
import statsmodels.api as sm
import statsmodels.formula.api as smf  
import seaborn as sns
import scipy.stats as ss
import matplotlib.pyplot as plt
import plotly.figure_factory as ff
import plotly
import statsmodels.api as sm
from urllib.request import urlopen
import json
with urlopen('https://raw.githubusercontent.com/plotly/datasets/master/geojson-counties-fips.json') as response:
    counties = json.load(response)
import plotly.express as px
from sklearn.preprocessing import normalize, StandardScaler
import sklearn.metrics as sklm
import patsy
from patsy import dmatrices
from sklearn import metrics
from math import sqrt
import statsmodels.tsa.seasonal as sts
import statsmodels.graphics.tsaplots as splt
import pymc3 as pm
import arviz as az
from statsmodels.graphics.regressionplots import influence_plot, plot_regress_exog
WARNING (theano.tensor.blas): Using NumPy C-API based implementation for BLAS functions.
In [3]:
# Load datasets
affinity = pd.read_csv("data/affinity_county.csv")
employment = pd.read_csv("data/employment_county.csv")
womply = pd.read_csv("data/womply_county.csv")
ui_claims = pd.read_csv("data/ui_claims_county.csv")
mobility = pd.read_csv("data/Google Mobility - County - Daily.csv")

usps_2018 = pd.read_csv("data/Y2018.csv")
usps_2019 = pd.read_csv("data/Y2019.csv")
usps_2020 = pd.read_csv("data/Y2020.csv")
usps_2021 = pd.read_csv("data/Y2021.csv")
usps_2022 = pd.read_csv("data/Y2022.csv")

population = pd.read_csv("data/geodata_county.csv") ## population data also from Opportunity Insights
zip_cty_crosswalk = pd.read_csv("data/ZIP_COUNTY_122021.csv", dtype={'zip': str})

All of the Opportunities Insights data is relative to a baseline of January 2020. The values for these data are the percent change in the variable from January 2020 levels. In the cases of credit/debit card spending, small business openings, and small business revenues, these values are also seasonally adjusted. Most of the data is either weekly or daily, but the USPS data is only monthly, so I aggregate each of the datasets by taking the mean percent change by month/county.

In [4]:
affinity['spend_all'].replace(".", "NaN", inplace=True)
affinity['spend_all'] = affinity['spend_all'].astype(float)
affinity = affinity.groupby(['year', 'month', 'countyfips'])[['spend_all']].mean().reset_index()
affinity = affinity.dropna()
In [5]:
# More expansive list of employment variables if desired.
#emp_vars = ['emp', 'emp_incq1', 'emp_incq2', 'emp_incq3', 'emp_incq4', 'emp_incmiddle', 'emp_incbelowmed', 'emp_incabovemed']

emp_vars = ['emp']
for var in emp_vars:
    employment[var].replace(".", "NaN", inplace=True)
    employment[var] = employment[var].astype(float)
employment = employment.groupby(['year', 'month', 'countyfips'])[emp_vars].mean().reset_index()
employment = employment.dropna()
In [6]:
womply = womply.groupby(['year', 'month', 'countyfips'])[['merchants_all', 'revenue_all']].mean().reset_index()
womply = womply.dropna()
In [7]:
ui_claims_vars = ['initclaims_count_regular', 'initclaims_rate_regular']
for var in ui_claims_vars:
    ui_claims[var].replace(".", "NaN", inplace=True)
    ui_claims[var] = ui_claims[var].astype(float)
ui_claims = ui_claims.groupby(['year', 'month', 'countyfips'])[ui_claims_vars].mean().reset_index()
ui_claims = ui_claims.dropna()
In [8]:
# More expansive list of mobility variables if desired.
#mobility_vars = ['gps_retail_and_recreation', 'gps_grocery_and_pharmacy', 'gps_parks', 'gps_transit_stations', 'gps_workplaces', 'gps_residential', 'gps_away_from_home']
mobility_vars = ['gps_retail_and_recreation', 'gps_away_from_home']

for var in mobility_vars:
    mobility[var].replace(".", "NaN", inplace=True)
    mobility[var] = mobility[var].astype(float)

mobility = mobility.groupby(['year', 'month', 'countyfips'])[mobility_vars].mean().reset_index()

The USPS data is at the ZIP code by month level. In order to aggregate this data to the county level, I use a ZIP code-to-county crosswalk file compiled by the U.S. Department of Housing and Urban Development.[7] This crosswalk contains the ratio of each ZIP code that lies in each county, by population. I therefore multiply the inflows and outflows by the ratio of each ZIP code that is in each county, then sum these values by county to aggregate the data. Additionally, I use 2019 flows as a baseline in my analysis, so I handle the USPS data for that year separately and then merge the 2019 data as its own column in the eventual dataframe.

In [9]:
usps = pd.concat([usps_2018, usps_2019, usps_2020, usps_2021, usps_2022], ignore_index=True)
usps['ZIPCODE'] = usps['ZIPCODE'].str[2:7]
usps['year'] = usps['YYYYMM'].astype(str).str[:4].astype(int)
usps['month'] = usps['YYYYMM'].astype(str).str[4:6].astype(int)
usps = usps.dropna()

# 2019 USPS data.
usps_2019['ZIPCODE'] = usps_2019['ZIPCODE'].str[2:7]
usps_2019['year'] = usps_2019['YYYYMM'].astype(str).str[:4].astype(int)
usps_2019['month'] = usps_2019['YYYYMM'].astype(str).str[4:6].astype(int)
usps_2019 = usps_2019.dropna()

zip_cty_crosswalk = zip_cty_crosswalk[['zip', 'county', 'tot_ratio']]
zip_cty_crosswalk =zip_cty_crosswalk.dropna()

# Merge USPS data (zip code level) with crosswalk
usps = usps.merge(zip_cty_crosswalk, left_on='ZIPCODE', right_on='zip')

# Multiply flow variables by the share of the zip code in each county
usps['total_from_cty'] = usps['TOTAL FROM ZIP'] * usps['tot_ratio']
usps['total_to_cty'] = usps['TOTAL TO ZIP'] * usps['tot_ratio']

usps['countyfips'] = usps['county']

# Aggregate to county-level
usps = usps.groupby(['year', 'month', 'countyfips'])['total_from_cty', 'total_to_cty'].sum().reset_index()

usps.count()

# Merge in 2019 USPS data as a baseline
usps_2019 = usps_2019.merge(zip_cty_crosswalk, left_on='ZIPCODE', right_on='zip')
usps_2019['total_from_cty2019'] = usps_2019['TOTAL FROM ZIP'] * usps_2019['tot_ratio']
usps_2019['total_to_cty2019'] = usps_2019['TOTAL TO ZIP'] * usps_2019['tot_ratio']
usps_2019['countyfips'] = usps_2019['county']
usps_2019 = usps_2019.groupby(['year', 'month', 'countyfips'])['total_from_cty2019', 'total_to_cty2019'].sum().reset_index()

usps_2019 = usps_2019[['month', 'countyfips', 'total_from_cty2019', 'total_to_cty2019']]

usps = usps.merge(usps_2019, on=['month', 'countyfips'])

usps.sort_values(['year', 'month', 'countyfips']).head()
C:\Users\nloreedwards\AppData\Local\Temp\ipykernel_34684\174033804.py:26: FutureWarning: Indexing with multiple keys (implicitly converted to a tuple of keys) will be deprecated, use a list instead.
  usps = usps.groupby(['year', 'month', 'countyfips'])['total_from_cty', 'total_to_cty'].sum().reset_index()
C:\Users\nloreedwards\AppData\Local\Temp\ipykernel_34684\174033804.py:35: FutureWarning: Indexing with multiple keys (implicitly converted to a tuple of keys) will be deprecated, use a list instead.
  usps_2019 = usps_2019.groupby(['year', 'month', 'countyfips'])['total_from_cty2019', 'total_to_cty2019'].sum().reset_index()
Out[9]:
year month countyfips total_from_cty total_to_cty total_from_cty2019 total_to_cty2019
0 2018 11 1001 365.088912 363.712894 339.555358 340.142604
4 2018 11 1003 1700.826484 2786.519204 1717.071875 2661.439299
8 2018 11 1005 115.754246 96.770215 103.476315 89.021602
12 2018 11 1007 106.764231 103.171038 77.189013 87.767661
16 2018 11 1009 274.853212 291.433352 285.272484 308.189213

I finally merge together the various datasets and calculate the net flows from the USPS and population variables. I have two main netflows variables. The first, 'net_flows_pop', measures the net flows as a percent of the county population. In this case, a value of 1% would mean that in that month, on net, a number of people equivalent to 1% of the county's population in 2019 moved into the county. The second main variable I calculate, 'net_flow_rel2019', performs this same calculation for the 2019 data, then subtracts the monthly 2019 net flows from the 'net_flows_pop' variable. This is meant to account for some seasonality in net flows. For example, people moving from the northeast to Florida during the winter. The 'net_flow_rel2019' variable therefore measures any net flows that are above or below what would be expected based on 2019 data.

In [10]:
df = affinity.merge(employment, on=['year', 'month', 'countyfips'], how='outer')
df = df.merge(womply, on=['year', 'month', 'countyfips'], how='outer')
df = df.merge(ui_claims, on=['year', 'month', 'countyfips'], how='outer')
df = df.merge(mobility, on=['year', 'month', 'countyfips'], how='outer')
df = df.merge(usps, on=['year', 'month', 'countyfips'], how='outer')
df = df.merge(population, on='countyfips', how='outer')
df = df[(df['year'] > 2019)]

# Net flows var 1
df['net_flow'] = df['total_to_cty'] - df['total_from_cty']
df['net_flow_pop'] = (df['net_flow'] / df['county_pop2019']) * 100

# Net flows var 2
df['net_flow2019'] = df['total_to_cty2019'] - df['total_from_cty2019']
df['net_flow_pop2019'] = (df['net_flow2019'] / df['county_pop2019']) * 100
df['net_flow_rel2019'] = df['net_flow_pop'] - df['net_flow_pop2019']

df['cty_str'] = df['countyfips'].astype(str)
df.loc[df['statefips'] < 10, 'cty_str'] = "0" + df['cty_str']

# Convert share variables to percentages
for var in ['spend_all', 'emp', 'merchants_all', 'revenue_all', 'gps_retail_and_recreation', 'gps_away_from_home']:
    df[var] = df[var] * 100

df.to_csv('data/test.csv')
df.sort_values(['year', 'month', 'countyfips']).head()
df.describe()
Out[10]:
year month countyfips spend_all emp merchants_all revenue_all initclaims_count_regular initclaims_rate_regular gps_retail_and_recreation ... total_to_cty2019 cityid cz statefips county_pop2019 net_flow net_flow_pop net_flow2019 net_flow_pop2019 net_flow_rel2019
count 106892.000000 106892.000000 106892.000000 57067.000000 42360.000000 19552.000000 19552.000000 37212.000000 37212.000000 55504.000000 ... 103675.000000 1938.000000 104525.000000 104525.000000 1.045250e+05 103675.000000 101308.000000 103675.000000 101308.000000 101308.000000
mean 2020.935299 6.195936 31292.100475 6.199427 -4.208388 -4.608527 -1.032096 352.184748 0.513510 -2.569137 ... 881.069217 25.245614 20185.859364 30.268271 1.067176e+05 -37.859199 -0.025622 -49.007567 -0.068830 0.043208
std 0.800843 3.319029 16196.233089 17.071393 17.606782 13.982371 37.251369 2399.814440 0.849029 17.294122 ... 2779.877114 16.077752 11177.801706 15.142605 3.367098e+05 534.913761 0.309206 510.171591 0.350811 0.226735
min 2020.000000 1.000000 1001.000000 -84.530000 -121.000000 -65.300000 -96.460000 0.000000 0.000000 -92.260000 ... 0.000000 1.000000 100.000000 1.000000 1.690000e+02 -27809.816196 -9.118810 -20511.605568 -15.300584 -10.302418
25% 2020.000000 3.000000 19021.000000 -3.504150 -11.650000 -12.975000 -24.021250 12.000000 0.123050 -11.768039 ... 65.382789 11.000000 10502.000000 18.000000 1.185300e+04 -32.392757 -0.111772 -49.740641 -0.157032 -0.035696
50% 2021.000000 6.000000 29223.000000 6.099903 -4.471000 -3.760250 -3.842000 37.419000 0.258250 -2.689247 ... 181.955402 25.000000 21301.000000 29.000000 2.672900e+04 -3.890376 -0.021660 -11.995423 -0.054775 0.032566
75% 2022.000000 9.000000 46105.000000 16.609188 2.510000 2.801525 15.608313 135.750000 0.555000 6.324070 ... 552.230981 39.000000 29502.000000 45.000000 7.046100e+04 14.284271 0.060722 6.250270 0.025746 0.118260
max 2022.000000 12.000000 78030.000000 72.600000 201.200000 81.800000 376.000000 188433.500000 30.060000 282.451613 ... 71885.938373 53.000000 39400.000000 56.000000 1.003911e+07 20993.788626 12.260596 23095.785287 13.559546 7.409221

8 rows × 24 columns

In [11]:
df[df['year'] == 2020].count()
Out[11]:
year                         37959
month                        37959
countyfips                   37959
spend_all                    20812
emp                          16944
merchants_all                 9024
revenue_all                   9024
initclaims_count_regular     16192
initclaims_rate_regular      16192
gps_retail_and_recreation    19957
gps_away_from_home           16367
total_from_cty               37758
total_to_cty                 37758
total_from_cty2019           37758
total_to_cty2019             37758
countyname                   37087
cityid                         684
cityname                       684
cz                           37087
czname                       37087
statename                    37087
statefips                    37087
stateabbrev                  37087
county_pop2019               37087
net_flow                     37758
net_flow_pop                 36886
net_flow2019                 37758
net_flow_pop2019             36886
net_flow_rel2019             36886
cty_str                      37959
dtype: int64
In [12]:
# Add time variable
df['time'] = df['year'].astype(str).str[:-2] + "-" + df['month'].astype(str).str[:-2]

## Create a datetime type column and a decimal year column
def date_to_decimal(x,frac=1.0/12.0):
    return x.year + frac * x.month
df.loc[:,'time'] = pd.to_datetime(df.loc[:,'time'])
df.loc[:,'time_decimal'] = df.loc[:,'time'].map(date_to_decimal)
df.loc[:5,['time','time_decimal']]
Out[12]:
time time_decimal
0 2020-01-01 2020.083333
1 2020-02-01 2020.166667
2 2020-03-01 2020.250000
3 2020-04-01 2020.333333
4 2020-05-01 2020.416667
5 2020-06-01 2020.500000
In [13]:
# Create dataset of USPS vars
df_usps = usps.merge(population, on='countyfips', how='inner')
#df_usps.dropna()

# Net flows var 1
df_usps['net_flow'] = df_usps['total_to_cty'] - df_usps['total_from_cty']
df_usps['net_flow_pop'] = (df_usps['net_flow'] / df_usps['county_pop2019']) * 100

# Net flows var 2
df_usps['net_flow2019'] = df_usps['total_to_cty2019'] - df_usps['total_from_cty2019']
df_usps['net_flow_pop2019'] = (df_usps['net_flow2019'] / df_usps['county_pop2019']) * 100
df_usps['net_flow_rel2019'] = df_usps['net_flow_pop'] - df_usps['net_flow_pop2019']

df_usps['cty_str'] = df_usps['countyfips'].astype(str)
df_usps.loc[df_usps['statefips'] < 10, 'cty_str'] = "0" + df_usps['cty_str']

df_usps['time'] = df_usps['year'].astype(str) + "-" + df_usps['month'].astype(str)
df_usps.loc[:,'time'] = pd.to_datetime(df_usps.loc[:,'time'])
df_usps.loc[:,'time_decimal'] = df_usps.loc[:,'time'].map(date_to_decimal)
df_usps = df_usps.sort_values(['countyfips', 'year', 'month']).reset_index()
df_usps.head()
Out[13]:
index year month countyfips total_from_cty total_to_cty total_from_cty2019 total_to_cty2019 countyname cityid ... stateabbrev county_pop2019 net_flow net_flow_pop net_flow2019 net_flow_pop2019 net_flow_rel2019 cty_str time time_decimal
0 0 2018 11 1001 365.088912 363.712894 339.555358 340.142604 Autauga NaN ... AL 55869 -1.376019 -0.002463 0.587246 0.001051 -3.514050e-03 01001 2018-11-01 2018.916667
1 4 2018 12 1001 316.423892 310.214802 302.622248 292.433546 Autauga NaN ... AL 55869 -6.209090 -0.011114 -10.188702 -0.018237 7.123113e-03 01001 2018-12-01 2019.000000
2 8 2019 1 1001 363.567918 394.407545 363.567918 394.407545 Autauga NaN ... AL 55869 30.839627 0.055200 30.839627 0.055200 0.000000e+00 01001 2019-01-01 2019.083333
3 12 2019 2 1001 430.134618 361.700908 430.134618 361.700908 Autauga NaN ... AL 55869 -68.433710 -0.122490 -68.433710 -0.122490 1.110223e-16 01001 2019-02-01 2019.166667
4 16 2019 3 1001 477.855789 424.394354 477.855789 424.394354 Autauga NaN ... AL 55869 -53.461435 -0.095691 -53.461435 -0.095691 1.110223e-16 01001 2019-03-01 2019.250000

5 rows × 25 columns

Data Visualizations¶

Handling Missing Data¶

First, I examine the missing data in the combined dataset. Given the multiple sources, varied data completeness across these sources, and the timeline of this data, there is likley a substantial amount of missing data. Limiting the analysis to only observations with complete data across all variables could bias the result if counties with missing data are more populous, for example.

To try and understand how data availability may bias my results, I first look at summary statistics for the full dataset and the dataset when conditioning on containing the key economic variables (hereafter: the "subsample"), which tend to have the most missing data. The below tables show these sets of summary statistics, with the first table representing the full dataset.

A key difference that may help explain the other differences between these two tables is in the county population variable. In the subsample, the average county population is over 3x as large as in the full data. This shows that many of the counties being dropped by conditioning on economic variables are smaller counties, possibly where this data is more difficult to collect. The values of the economic variables tend to have lower standard deviations, likely because these variables are relative to January 2020 baselines. In smaller counties with less data, percent differences can be more extreme due to small sample size bias. This is also observed for the net flow variables that are relative to population.

In [14]:
econ_vars = ['spend_all', 'revenue_all', 'emp', 'gps_retail_and_recreation']
df[np.append(econ_vars, ['county_pop2019', 'net_flow', 'net_flow_pop', 'net_flow2019', 'net_flow_pop2019', 'net_flow_rel2019'])].describe()
Out[14]:
spend_all revenue_all emp gps_retail_and_recreation county_pop2019 net_flow net_flow_pop net_flow2019 net_flow_pop2019 net_flow_rel2019
count 57067.000000 19552.000000 42360.000000 55504.000000 1.045250e+05 103675.000000 101308.000000 103675.000000 101308.000000 101308.000000
mean 6.199427 -1.032096 -4.208388 -2.569137 1.067176e+05 -37.859199 -0.025622 -49.007567 -0.068830 0.043208
std 17.071393 37.251369 17.606782 17.294122 3.367098e+05 534.913761 0.309206 510.171591 0.350811 0.226735
min -84.530000 -96.460000 -121.000000 -92.260000 1.690000e+02 -27809.816196 -9.118810 -20511.605568 -15.300584 -10.302418
25% -3.504150 -24.021250 -11.650000 -11.768039 1.185300e+04 -32.392757 -0.111772 -49.740641 -0.157032 -0.035696
50% 6.099903 -3.842000 -4.471000 -2.689247 2.672900e+04 -3.890376 -0.021660 -11.995423 -0.054775 0.032566
75% 16.609188 15.608313 2.510000 6.324070 7.046100e+04 14.284271 0.060722 6.250270 0.025746 0.118260
max 72.600000 376.000000 201.200000 282.451613 1.003911e+07 20993.788626 12.260596 23095.785287 13.559546 7.409221
In [15]:
df_nonmissing = df.dropna(subset=econ_vars)
df_nonmissing[np.append(econ_vars, ['county_pop2019', 'net_flow', 'net_flow_pop', 'net_flow2019', 'net_flow_pop2019', 'net_flow_rel2019'])].describe()
Out[15]:
spend_all revenue_all emp gps_retail_and_recreation county_pop2019 net_flow net_flow_pop net_flow2019 net_flow_pop2019 net_flow_rel2019
count 16347.000000 16347.000000 16347.000000 16347.000000 1.634700e+04 16347.000000 16347.000000 16347.000000 16347.000000 16347.000000
mean 2.143200 -1.234776 -6.447956 -8.731661 3.752753e+05 -115.844686 -0.011366 -138.970242 -0.042074 0.030709
std 14.313654 37.098562 11.410277 16.216664 6.438388e+05 1158.034478 0.242659 1097.991991 0.272159 0.123248
min -68.770000 -96.460000 -63.325000 -85.570000 2.563800e+04 -27809.816196 -3.912901 -20511.605568 -3.885441 -1.571345
25% -6.201774 -24.575000 -12.150000 -16.835484 1.038060e+05 -212.873541 -0.088525 -263.490062 -0.111237 -0.016855
50% 2.597645 -5.065250 -6.928000 -8.257774 1.807420e+05 -33.130454 -0.019764 -75.196873 -0.039671 0.021705
75% 11.230500 16.486500 -0.995375 -0.447694 3.983290e+05 85.090620 0.054757 41.727476 0.027774 0.067808
max 68.742857 328.000000 117.250000 282.451613 1.003911e+07 20993.788626 2.908731 23095.785287 2.928796 3.688559

I next explore how the selection of counties may change over time in the subsample. It is possible that over time, the number of counties and/or the composition of counties included in the data changes. This would impact the results, as we couldn't be certain that any changes over time were due to genuine changes in the variable, or if they were due to sample changes. I create the following figures to assess this potential issue:

In [16]:
year_month_obs = df_nonmissing.groupby(['time']).count()
county_obs = df_nonmissing.groupby(['countyfips']).count()

fig, ax = plt.subplots(1,2, figsize=(16,8))
ax[0] = sns.scatterplot(data= year_month_obs, x='time', y='countyfips', ax=ax[0])
ax[0].set_ylabel('Number of Counties')
ax[0].set_xlabel("Year-Month")
ax[0].set_title('Number of Counties in Non-Missing Data Over Time')

ax[1] = sns.histplot(data= county_obs, x='time', ax=ax[1])
ax[1].set_ylabel("Number of counties with each number of observations")
ax[1].set_xlabel("Number of observations")
ax[1].set_title('Number of Year-Months per County')
Out[16]:
Text(0.5, 1.0, 'Number of Year-Months per County')

We see from the first figure that the number of counties in the data is pretty consistent over time. There is a slight drop in observations from 657 to 654, then to 653, but these are minor changes given the sample size. Another concern is that the composition of counties varies over time, though the second figure addresses this concern. Since the number of year-months represented by almost every county is 25, we know they have an observation in each year-month combination. To make this a perfectly balanced dataset, I exclude the 4 counties without complete information over time:

In [17]:
kept_counties = county_obs[county_obs['time'] == 25]

df_nonmissing = df_nonmissing.merge(kept_counties.reset_index()['countyfips'], on='countyfips', how='inner')

Finally, I look at the geographical distribution of this new list, and find that states along the coast tend to have counties with data, while states in the middle of the country are largely underrepresented. The main purpose of this map is to see where we have complete data, but I also show the preferred net flow variable for June, 2020.

In [18]:
fig = px.choropleth(df_nonmissing[df_nonmissing['time_decimal'] == 2020.5], 
    geojson=counties, 
    locations='cty_str', 
    color='net_flow_rel2019',
    color_continuous_scale="RdYlGn",
    range_color=(-1,1),
    scope="usa",
    title="June 2020 Net Flows, relative to Population, 2019 Baseline",
    labels={'net_flow_rel2019':'Net Flows'}
)
fig.update_layout(margin={"r":0,"t":0,"l":0,"b":0})

# Improve the legend
fig.update_layout(coloraxis_colorbar=dict(
    thicknessmode="pixels", thickness=10,
    lenmode="pixels", len=150,
    ticks="outside", ticksuffix=" %",
))

fig.show()
−1 %−0.5 %0 %0.5 %1 %Net FlowsJune 2020 Net Flows, relative to Population, 2019 Baseline
plotly-logomark

The main dataset I'll use for my analysis is the subsample, given the need for economic variables in order to perform my later regressions. This means that the conclusions I draw from this data are not necessarily generalizable for the entire US population, but will encompass the counties above.

Data relationships¶

I start with a simple representation of data for one county, New York City, over the timeseries of the data. I plot the net migration flows and several economic variables side-by-side to see how closely they follow one another over time. These figures show how NYC experienced a dramatic net outflow during the pandemic, in addition to economic losses across all variables. For most of the economic activity variables, they seem to follow the net flows through 2020 and some of 2021, but the relationship changes when net flows plateau. The economic variables continue to recover, but we don't observe a major return to NYC, which would be represented by positive net flows that equal the negative flows in magnitude. Instead, people just stop leaving NYC in mid-2021. The economic activity variable that most closely resembles this pattern is the GPS data on time spent at retail and recreation businesses, which also starts to plateau at a similar point. This may indicate that net flows are more relevant for predicting economic activty during the pandemic than after, or that we must account for previous net flows when predicting economic activity.

In [19]:
y_vars = ['net_flow_rel2019', 'spend_all', 'revenue_all', 'emp', 'gps_retail_and_recreation', 'initclaims_rate_regular']

labels = ['Net Flows (% of population) rel. 2019', 'Avg. Credit/Debit Card Spending rel. Jan 2020 (%)', 'Avg. Small Business Revenue rel. Jan 2020 (%)', 'Avg. Employment rel. Jan 2020 (%)', 'Avg. Time at Retail/Recreation rel. Jan 2020 (%)', 'Unemployment claims per 100 people (rel. 2019 levels)']

fig, ax = plt.subplots(3,2, figsize=(16,16))
ax = ax.flatten()
for i,y in enumerate(y_vars):
    ax[i] = sns.scatterplot(data= df[df['countyfips'] == 36061], x='time', y=y, ax=ax[i])
    ax[i].set_ylabel(labels[i])
    ax[i].set_xlabel("Year-Month")
    
plt.show()

To get a sense of overall trends in the data, I aggregate the monthly data to yearly data. This makes it a bit easier to understand how data in 2020 compares to data in 2021 and 2022 on average. I choose to take the mean of the net flow variables rather than calculating the total net flows by year so that I can compare average monthly changes in flows to average monthly changes in economic variables.

In [20]:
yearly_nf = df.groupby(['year', 'countyfips', 'cty_str'])[['net_flow_pop', 'net_flow_rel2019']].mean().reset_index()
yearly_nf = yearly_nf.merge(population, on='countyfips')
In [21]:
yearly_rev = df.groupby(['year', 'countyfips', 'cty_str', 'statefips'])[['revenue_all', 'spend_all', 'merchants_all', 'gps_away_from_home', 'gps_retail_and_recreation', 'emp']].mean().reset_index()
In [22]:
yearly_df = yearly_nf.merge(yearly_rev, on=['year', 'countyfips', 'cty_str', 'statefips'], how='outer')

yearly_df.head()
Out[22]:
year countyfips cty_str net_flow_pop net_flow_rel2019 countyname cityid cityname cz czname statename statefips stateabbrev county_pop2019 revenue_all spend_all merchants_all gps_away_from_home gps_retail_and_recreation emp
0 2020.0 1001 01001 0.008185 0.068750 Autauga NaN NaN 11101.0 Montgomery Alabama 1 AL 55869 NaN -2.157843 NaN -7.312443 -4.630892 -5.736236
1 2021.0 1001 01001 -0.026920 0.033645 Autauga NaN NaN 11101.0 Montgomery Alabama 1 AL 55869 NaN 22.429551 NaN -5.507566 -2.807211 5.544250
2 2022.0 1001 01001 -0.019293 0.047090 Autauga NaN NaN 11101.0 Montgomery Alabama 1 AL 55869 NaN 28.966813 NaN -5.336718 -2.625255 -5.449417
3 2020.0 1003 01003 0.194242 0.008701 Baldwin NaN NaN 11001.0 Mobile Alabama 1 AL 223234 0.346979 -7.224176 -6.454085 -4.478898 -4.151259 -3.955978
4 2021.0 1003 01003 0.179190 -0.006350 Baldwin NaN NaN 11001.0 Mobile Alabama 1 AL 223234 34.271917 7.769365 -3.811577 -2.931887 9.542184 17.149583

I next consider how county data varies across and within states by looking at ordered boxplots of the yearly data. I plot data for the net flows (relative to population) and credit-debit card spending (rel. January 2020).

In [23]:
sorted_index = yearly_df[yearly_df['year']==2020].groupby(['stateabbrev'])['net_flow_pop'].median().sort_values().index

fig, ax = plt.subplots(figsize=(12, 12))  
fig.subplots_adjust(bottom=0.1)
_=sns.boxenplot(x='stateabbrev', y='net_flow_pop', color='lightgray', data=yearly_df[yearly_df['year']==2020], order=sorted_index)
_=ax.set_xticklabels(ax.get_xticklabels(), rotation=90)
_=ax.set_title('Net Flows (rel. Population) by State (2020)')
_=ax.set_xlabel('State')
_=ax.set_ylabel('Net Flows (rel. Population)')
In [24]:
sorted_index = yearly_df[yearly_df['year']==2020].groupby(['stateabbrev'])['spend_all'].median().sort_values().index

fig, ax = plt.subplots(figsize=(12, 12))  
fig.subplots_adjust(bottom=0.1)
_=sns.boxenplot(x='stateabbrev', y='spend_all', color='lightgray', data=yearly_df[yearly_df['year']==2020], order=sorted_index)
_=ax.set_xticklabels(ax.get_xticklabels(), rotation=90)
_=ax.set_title('Spending rel. Jan 2020 by State (2020)')
_=ax.set_xlabel('State')
_=ax.set_ylabel('Spending rel. Jan 2020')

These boxplots show that there is a lot of variation of economic variables and migration variables within a state. They also show that the states with the greatest net outflows are not necessarily the states with the greatest drop in credit/debit card spending.

For a more robust analysis of how economic variables may be related to the USPS net flows, I plot the correlations between our primary economic variables and the migration variables by year, at the county-level. This allows me to see which variables have the strongest correlation with migration and whether these correlations change over time.

In [25]:
labels = ["Avg. Credit/Debit Card Spending rel. Jan 2020 (%)", "Avg. Time at Retail/Recreation rel. Jan 2020 (%)", "Avg. Employment rel. Jan 2020 (%)", "Avg. Small Business Revenue rel. Jan 2020 (%)"]
k = 0
fig, ax = plt.subplots(4,3, figsize=(16,20))
ax = ax.flatten()
for i,y in enumerate(['spend_all', 'gps_retail_and_recreation', 'emp', 'revenue_all']):
    for j,year in enumerate([2020, 2021, 2022]):
        ax[k] = sns.regplot(data=yearly_df[yearly_df['year'] == year], x='net_flow_pop', y=y, scatter_kws={'s':3,'alpha':0.2}, ax=ax[k])
        ax[k].set_title("Data From:" + str(year))
        ax[k].set_ylabel(labels[i])
        ax[k].set_xlabel("Yearly Net Flows rel. 2019 Population (%)")
        k = k+1

Time spent at retail/recreation seems to have the most consistently positive correlation with net flows over time. In 2020, there is also a strong positive correlation between small business revenues and net flows, but the regression line becomes much flatter in 2021 and 2022. These changes in correlations over time indicate that certain variables may be more useful predictors in 2020 than in later years.

Given the different effects of COVID across states, which includes the impacts of state policy and COVID prevalence, it is reasonable to think that these correlations may differ by state. To get a sense of this variation, I choose to compare counties in New York and Florida, two large states with different COVID policy and net migration flows. I reproduce the above figure, but just with data from these states, and plot the regression lines corresponding to the data from each state.

In [26]:
labels = ["Avg. Credit/Debit Card Spending rel. Jan 2020 (%)", "Avg. Time at Retail/Recreation rel. Jan 2020 (%)", "Avg. Employment rel. Jan 2020 (%)", "Avg. Small Business Revenue rel. Jan 2020 (%)"]
k = 0
fig, ax = plt.subplots(4,3, figsize=(16,20))
ax = ax.flatten()
for i,y in enumerate(['spend_all', 'gps_retail_and_recreation', 'emp', 'revenue_all']):
    for j,year in enumerate([2020, 2021, 2022]):
        ax[k] = sns.regplot(data=yearly_df[(yearly_df['year'] == year) & (yearly_df['statefips'] == 36)], y='net_flow_pop', x=y, scatter_kws={'s':6,'alpha':1}, ax=ax[k])
        ax[k] = sns.regplot(data=yearly_df[(yearly_df['year'] == year) & (yearly_df['statefips'] == 12)], y='net_flow_pop', x=y, scatter_kws={'s':6,'alpha':1, 'color': 'orange'}, ax=ax[k])
        ax[k].set_title("Data From:" + str(year))
        ax[k].set_xlabel(labels[i])
        ax[k].set_ylabel("Yearly Net Flows rel. 2019 Population (%)")
        k = k+1
        
plt.figlegend(labels=['NY', '', '', 'FL', '', ''], loc="upper left", title="State of County")
plt.tight_layout()
        
plt.show()

It's clear from these figures that the relationships between economic indicators and net flows differ across states, and in some cases even have opposite correlations. In general, the correlations for New York and Florida are more similar in 2021 and 2022 than they are in 2020, likely due to NYC being an extreme outlier in terms of net migration flows. This has several implications for a potential model that would use new migration flows as a predictor of other economic variables. First, the model may need to consider state-level or county-level fixed effects when making its predictions, as the strength and even direction of the relationship between economic indicators and migration varies by state. Second, data from 2020 may be misleading for predicting future trends, given the impact of the initial lockdown. Some version of a time fixed-effect should be used when performing a more robust analysis of the correlations between economic variables and migration flows.

Finally, to get a sense of how net flows vary across the US, I map the yearly total net flows across counties for 2020 and 2021. These maps show similar patterns overall, with a few differences. It appears that 2021 has fewer extreme values than 2020, as observed by lighter shades of green and red. Additionally, zooming in on the counties of major cities shows an exodus from those counties in 2020, with a sustained but less extreme exodus in 2021.

In [27]:
yearly_nf_agg = df.groupby(['year', 'countyfips', 'cty_str'])[['total_to_cty', 'total_from_cty']].sum().reset_index()

yearly_nf_agg = yearly_nf_agg.merge(population, on='countyfips')

yearly_nf_agg['net_flow'] = yearly_nf_agg['total_to_cty'] - yearly_nf_agg['total_from_cty']
yearly_nf_agg['net_flow_pop'] = (yearly_nf_agg['net_flow'] / yearly_nf_agg['county_pop2019']) * 100
In [28]:
fig = px.choropleth(yearly_nf_agg[yearly_nf_agg['year'] == 2020], 
    geojson=counties, 
    locations='cty_str', 
    color='net_flow_pop',
    color_continuous_scale="RdYlGn",
    range_color=(-2,2),
    scope="usa",
    labels={'net_flow_pop':'Net Flow (rel. Population)'}
)
fig.update_layout(margin={"r":0,"t":0,"l":0,"b":0})

# Improve the legend
fig.update_layout(coloraxis_colorbar=dict(
    thicknessmode="pixels", thickness=10,
    lenmode="pixels", len=150,
    ticks="outside", ticksuffix=" %",
))

fig.show()
−2 %−1 %0 %1 %2 %Net Flow (rel. Population)
plotly-logomark
In [29]:
fig = px.choropleth(yearly_nf_agg[yearly_nf_agg['year'] == 2021], 
    geojson=counties, 
    locations='cty_str', 
    color='net_flow_pop',
    color_continuous_scale="RdYlGn",
    range_color=(-2,2),
    scope="usa",
    labels={'net_flow_pop':'Net Flow (rel. Population)'}
)
fig.update_layout(margin={"r":0,"t":0,"l":0,"b":0})

# Improve the legend
fig.update_layout(coloraxis_colorbar=dict(
    thicknessmode="pixels", thickness=10,
    lenmode="pixels", len=150,
    ticks="outside", ticksuffix=" %",
))

fig.show()
−2 %−1 %0 %1 %2 %Net Flow (rel. Population)
plotly-logomark

Time Trends¶

To understand how the model may be impacted by seasonality and general trends, this section looks at the time trends of the endogenous and exogenous variables. From here on, I'll use the net migration flows as a percent of the county population as my primary migration variable. This is because I'd like to exploit the seasonal variation in this variable. If I used the variable relative to 2019, I'd be removing this variation prematurely.

First, I consider how the variables have changed with time nationally by aggregating across counties and plotting the timeseries.

In [30]:
df_nonmissing_yr = df_nonmissing.groupby(['time'])['spend_all', 'revenue_all', 'emp', 'gps_retail_and_recreation', 'initclaims_rate_regular'].mean().reset_index()

df_usps_yr = df_usps[['countyfips', 'year', 'month', 'total_to_cty', 'time']]
df_usps_yr = df_usps_yr.groupby(['year', 'month', 'time'])[['total_to_cty']].sum().reset_index()

df_nonmissing_yr = df_nonmissing_yr.merge(df_usps_yr, on='time', how='outer')
df_nonmissing_yr = df_nonmissing_yr.set_index('time')
C:\Users\nloreedwards\AppData\Local\Temp\ipykernel_34684\4043477698.py:1: FutureWarning:

Indexing with multiple keys (implicitly converted to a tuple of keys) will be deprecated, use a list instead.

In [31]:
y_vars = ['total_to_cty', 'spend_all', 'revenue_all', 'emp', 'gps_retail_and_recreation', 'initclaims_rate_regular']
labels = ['Total Migration', 'Avg. Credit/Debit Card Spending rel. Jan 2020 (%)', 'Avg. Small Business Revenue rel. Jan 2020 (%)', 'Avg. Employment rel. Jan 2020 (%)', 'Avg. Time at Retail/Recreation rel. Jan 2020 (%)', 'Unemployment claims per 100 people (rel. 2019 levels)']

fig, ax = plt.subplots(3,2, figsize=(16,16))
ax = ax.flatten()
for i,y in enumerate(y_vars):
    ax[i] = sns.lineplot(data= df_nonmissing_yr[y], x='time', y=df_nonmissing_yr[y], ax=ax[i])
    ax[i].set_ylabel(labels[i])
    ax[i].set_xlabel("Year-Month")
    
plt.show()

There appears to be strong seasonal variation in the total number of address changes nationally. Additionally, the time at retail and recreation also looks to have some seasonal behavior, after accounting for April of 2020. The other variables do not look to have as much seasonal variation as one would expect, though it's hard to tell given the small timeframe and the outlier in April 2020, which is consistent for all of the economic variables. Surprisingly, the migration variable does not look very different for 2020 compared to 2021, aside from a slight decline in address changes, on average.

To get a sense of whether these national averages are consistent across counties, I look at the trends for the top 5 and bottom 5 counties in the data by population.

In [32]:
top_counties = df_nonmissing[df_nonmissing['time'] == '2020-06-01'].sort_values('county_pop2019', ascending=False)['countyfips'][:5]
df_nonmissing_bigcity = df_nonmissing.merge(top_counties, on="countyfips", how="inner")
In [33]:
bottom_counties = df_nonmissing[df_nonmissing['time'] == '2020-06-01'].sort_values('county_pop2019', ascending=True)['countyfips'][:5]
df_nonmissing_small = df_nonmissing.merge(bottom_counties, on="countyfips", how="inner")
In [34]:
y_vars = ['net_flow_pop', 'spend_all', 'revenue_all', 'emp', 'gps_retail_and_recreation', 'initclaims_rate_regular']
labels = ['Net Flow (rel. pop)', 'Avg. Credit/Debit Card Spending rel. Jan 2020 (%)', 'Avg. Small Business Revenue rel. Jan 2020 (%)', 'Avg. Employment rel. Jan 2020 (%)', 'Avg. Time at Retail/Recreation rel. Jan 2020 (%)', 'Unemployment claims per 100 people (rel. 2019 levels)']

fig, ax = plt.subplots(3,2, figsize=(16,16))
ax = ax.flatten()
for i,y in enumerate(y_vars):
    ax[i] = sns.lineplot(data= df_nonmissing_bigcity, x='time', y=y, hue='countyname', ax=ax[i])
    ax[i].set_ylabel(labels[i])
    ax[i].set_xlabel("Year-Month")
    
plt.show()
In [35]:
fig, ax = plt.subplots(3,2, figsize=(16,16))
ax = ax.flatten()
for i,y in enumerate(y_vars):
    ax[i] = sns.lineplot(data= df_nonmissing_small, x='time', y=y, hue='countyname', ax=ax[i])
    ax[i].set_ylabel(labels[i])
    ax[i].set_xlabel("Year-Month")
    
plt.show()

While the counties tend to follow similar trends in general, there are clear differences in the levels of migration flows and economic variables. For the migration flow variable, there is also a clear difference in the seasonality of this variable across counties. For example, Maricopa County has large seasonal variation in its inflows and outflows, while the other large counties see smaller flutuations. This has implications for developing a model, showing that removing the seasonal and trend variation must happen at the county-level. Applying the same adjustments for every county would be inaccurate, given the large variation in migration flows between counties.

Overall, the trends in these data are quite interesting. The economic variables show the impact of COVID-19 much more clearly than the main migration variable. While we'd think economic recovery and migration would go hand-in-hand, these time plots show that the relationship may be more complex than that assumption. In the next section, I more formerly test the correlations between the economic variables and the migration variable.

Models¶

In [36]:
## Define Functions
# Functions are from Dr. Stephen Elston's Lesson 10 Workbook
def compute_metrics(y_true, y_predicted):
    ## Compute the usual metrics
    mse = sklm.mean_squared_error(y_true, y_predicted)
    rmse = sqrt(mse)
    mae = sklm.median_absolute_error(y_true, y_predicted)
    return mse, rmse, mae

def print_metrics(df_test, model, label_col='net_flow_std'):   
    df_test['predicted'] = model.predict(df_test)
    mse, rmse, mae = compute_metrics(df_test.dropna(subset='predicted').loc[:,label_col],df_test.loc[:,'predicted'].dropna())   
    print('MSE  = {0:6.3f}'.format(mse))
    print('RMSE = {0:6.3f}'.format(rmse))
    print('MAE  = {0:6.3f}'.format(mae))    


def residual_plot(df):
    plt.rc('font', size=12)
    fig, ax = plt.subplots(figsize=(8, 3), ) 
    RMSE = np.std(df.resids)
    sns.scatterplot(x='predicted', y='resids', data=df, ax=ax);
    plt.axhline(0.0, color='red', linewidth=1.0);
    plt.axhline(2.0*RMSE, color='red', linestyle='dashed', linewidth=1.0);
    plt.axhline(-2.0*RMSE, color='red', linestyle='dashed', linewidth=1.0);
    plt.title('Residuals vs. predicted');
    plt.xlabel('Predicted values');
    plt.ylabel('Residuals');
    plt.show()

def plot_resid_dist(df):
    resids = df.loc[:,'resids']
    plt.rc('font', size=12)
    fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(10, 3));
    ## Plot a histogram
    sns.histplot(x=resids, bins=20, kde=True, ax=ax[0]);
    ax[0].set_title('Histogram of residuals');
    ax[0].set_xlabel('Residual values');
    ## Plot the Q-Q Normal plot
    ss.probplot(resids, plot = ax[1]);
    ax[1].set_title('Q-Q Normal plot of residuals');
    plt.show();    

def compute_residuals(df, model, label_col='net_flow_std'):
    df['predicted'] = model.predict(df)
    df['resids'] = np.subtract(df.loc[:,'predicted'], df.loc[:,label_col]) 
    return df

def print_coefficient_comparision(mod, compare_mod):
    df = pd.DataFrame(compare_mod.params)  
    df = pd.concat([df, pd.Series(mod.params, index=df.index)], axis=1)
    df.columns = ['Compare model','Model']                
    print(df)
    comp_mag = np.linalg.norm(df.loc[:,'Compare model'])
    mag = np.linalg.norm(df.loc[:,'Model'])
    df.drop('Intercept', axis=0, inplace=True)
    comp_mag_nointercept = np.linalg.norm(df.loc[:,'Compare model'])
    mag_nointercept = np.linalg.norm(df.loc[:,'Model'])

    print('\nMagnitude of base model = {0:4.2f}  Without intercept = {1:4.2f}'.format(comp_mag, comp_mag_nointercept))
    print('Magnitude of new model = {0:4.2f}  Without intercept = {1:4.2f}'.format(mag, mag_nointercept))

Modeling the relationship between economic variables and change of address¶

From the above exploratory analysis, it is unclear whether there is a relationship between the economic indicators and the USPS data, and this relationship will certainly vary by county/state. To understand the relationships in the data, which may become useful when creating a timeseries forecast, I will use an OLS model.

For this analysis, which is simply to explore if there are robust relationships in the data, NOT to predict future trends, I first use the raw migration and economic variables. These will contain seasonal and trend components, which I address by including one-hot-encoded variables for each county and month. I introduce a more formal predictive model in future sections.

In [37]:
ols_formula_fe = 'net_flow_pop ~ spend_all + gps_retail_and_recreation + emp + revenue_all + C(countyfips) + C(month)'

ols_model = smf.ols(ols_formula_fe, data=df_nonmissing).fit()
print(ols_model.summary())
                            OLS Regression Results                            
==============================================================================
Dep. Variable:           net_flow_pop   R-squared:                       0.211
Model:                            OLS   Adj. R-squared:                  0.177
Method:                 Least Squares   F-statistic:                     6.278
Date:                Sat, 17 Dec 2022   Prob (F-statistic):               0.00
Time:                        19:56:20   Log-Likelihood:                 1880.1
No. Observations:               16325   AIC:                            -2424.
Df Residuals:                   15657   BIC:                             2720.
Df Model:                         667                                         
Covariance Type:            nonrobust                                         
=============================================================================================
                                coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------------------
Intercept                     0.2097      0.045      4.699      0.000       0.122       0.297
C(countyfips)[T.1055]        -0.1834      0.062     -2.940      0.003      -0.306      -0.061
C(countyfips)[T.1069]        -0.1856      0.063     -2.966      0.003      -0.308      -0.063
C(countyfips)[T.1073]        -0.2197      0.063     -3.500      0.000      -0.343      -0.097
C(countyfips)[T.1081]        -0.2225      0.062     -3.569      0.000      -0.345      -0.100
C(countyfips)[T.1089]        -0.1465      0.062     -2.345      0.019      -0.269      -0.024
C(countyfips)[T.1095]        -0.2127      0.063     -3.392      0.001      -0.336      -0.090
C(countyfips)[T.1097]        -0.1829      0.062     -2.934      0.003      -0.305      -0.061
C(countyfips)[T.1101]        -0.2600      0.063     -4.157      0.000      -0.383      -0.137
C(countyfips)[T.1115]        -0.1195      0.063     -1.903      0.057      -0.243       0.004
C(countyfips)[T.1117]        -0.1320      0.063     -2.103      0.035      -0.255      -0.009
C(countyfips)[T.1125]        -0.2475      0.062     -3.967      0.000      -0.370      -0.125
C(countyfips)[T.2020]        -0.2756      0.062     -4.414      0.000      -0.398      -0.153
C(countyfips)[T.2090]        -0.3461      0.062     -5.545      0.000      -0.468      -0.224
C(countyfips)[T.4005]        -0.2902      0.062     -4.650      0.000      -0.413      -0.168
C(countyfips)[T.4013]        -0.1268      0.063     -2.029      0.042      -0.249      -0.004
C(countyfips)[T.4015]         0.0357      0.062      0.572      0.567      -0.087       0.158
C(countyfips)[T.4017]        -0.0676      0.062     -1.085      0.278      -0.190       0.055
C(countyfips)[T.4019]        -0.1466      0.062     -2.346      0.019      -0.269      -0.024
C(countyfips)[T.4021]         0.0871      0.062      1.397      0.162      -0.035       0.209
C(countyfips)[T.4025]        -0.0629      0.062     -1.008      0.313      -0.185       0.059
C(countyfips)[T.5031]        -0.3051      0.062     -4.889      0.000      -0.427      -0.183
C(countyfips)[T.5045]        -0.1814      0.063     -2.900      0.004      -0.304      -0.059
C(countyfips)[T.5051]        -0.2637      0.063     -4.199      0.000      -0.387      -0.141
C(countyfips)[T.5143]        -0.2198      0.062     -3.524      0.000      -0.342      -0.098
C(countyfips)[T.6001]        -0.2971      0.063     -4.737      0.000      -0.420      -0.174
C(countyfips)[T.6007]        -0.2810      0.062     -4.501      0.000      -0.403      -0.159
C(countyfips)[T.6013]        -0.2070      0.063     -3.305      0.001      -0.330      -0.084
C(countyfips)[T.6017]        -0.1322      0.063     -2.109      0.035      -0.255      -0.009
C(countyfips)[T.6019]        -0.2213      0.063     -3.538      0.000      -0.344      -0.099
C(countyfips)[T.6023]        -0.2838      0.063     -4.531      0.000      -0.407      -0.161
C(countyfips)[T.6029]        -0.2130      0.062     -3.409      0.001      -0.335      -0.091
C(countyfips)[T.6037]        -0.2723      0.063     -4.348      0.000      -0.395      -0.150
C(countyfips)[T.6039]        -0.1491      0.062     -2.389      0.017      -0.271      -0.027
C(countyfips)[T.6041]        -0.2086      0.063     -3.322      0.001      -0.332      -0.086
C(countyfips)[T.6045]        -0.3139      0.063     -5.012      0.000      -0.437      -0.191
C(countyfips)[T.6047]        -0.2278      0.063     -3.634      0.000      -0.351      -0.105
C(countyfips)[T.6053]        -0.2366      0.063     -3.775      0.000      -0.359      -0.114
C(countyfips)[T.6059]        -0.2006      0.063     -3.206      0.001      -0.323      -0.078
C(countyfips)[T.6061]        -0.1178      0.063     -1.883      0.060      -0.240       0.005
C(countyfips)[T.6065]        -0.1349      0.063     -2.156      0.031      -0.258      -0.012
C(countyfips)[T.6067]        -0.2210      0.062     -3.536      0.000      -0.343      -0.098
C(countyfips)[T.6069]        -0.1585      0.063     -2.525      0.012      -0.281      -0.035
C(countyfips)[T.6071]        -0.1898      0.062     -3.038      0.002      -0.312      -0.067
C(countyfips)[T.6073]        -0.2298      0.063     -3.673      0.000      -0.352      -0.107
C(countyfips)[T.6075]        -0.5765      0.063     -9.124      0.000      -0.700      -0.453
C(countyfips)[T.6077]        -0.1735      0.063     -2.776      0.006      -0.296      -0.051
C(countyfips)[T.6081]        -0.3286      0.063     -5.234      0.000      -0.452      -0.206
C(countyfips)[T.6083]        -0.2203      0.063     -3.523      0.000      -0.343      -0.098
C(countyfips)[T.6085]        -0.2895      0.063     -4.618      0.000      -0.412      -0.167
C(countyfips)[T.6087]        -0.2654      0.063     -4.236      0.000      -0.388      -0.143
C(countyfips)[T.6089]        -0.2676      0.063     -4.274      0.000      -0.390      -0.145
C(countyfips)[T.6095]        -0.2248      0.063     -3.591      0.000      -0.347      -0.102
C(countyfips)[T.6099]        -0.2436      0.062     -3.903      0.000      -0.366      -0.121
C(countyfips)[T.6101]        -0.2384      0.063     -3.813      0.000      -0.361      -0.116
C(countyfips)[T.6107]        -0.2126      0.063     -3.391      0.001      -0.335      -0.090
C(countyfips)[T.6111]        -0.1922      0.063     -3.070      0.002      -0.315      -0.069
C(countyfips)[T.6113]        -0.2387      0.063     -3.812      0.000      -0.361      -0.116
C(countyfips)[T.8001]        -0.2162      0.062     -3.464      0.001      -0.338      -0.094
C(countyfips)[T.8005]        -0.2015      0.062     -3.225      0.001      -0.324      -0.079
C(countyfips)[T.8013]        -0.3919      0.063     -6.255      0.000      -0.515      -0.269
C(countyfips)[T.8014]        -0.1585      0.063     -2.534      0.011      -0.281      -0.036
C(countyfips)[T.8031]        -0.3065      0.063     -4.899      0.000      -0.429      -0.184
C(countyfips)[T.8035]        -0.0605      0.062     -0.968      0.333      -0.183       0.062
C(countyfips)[T.8037]        -0.2328      0.063     -3.724      0.000      -0.355      -0.110
C(countyfips)[T.8041]        -0.2560      0.063     -4.087      0.000      -0.379      -0.133
C(countyfips)[T.8045]        -0.2479      0.062     -3.975      0.000      -0.370      -0.126
C(countyfips)[T.8059]        -0.2318      0.062     -3.714      0.000      -0.354      -0.109
C(countyfips)[T.8077]        -0.2325      0.062     -3.732      0.000      -0.355      -0.110
C(countyfips)[T.8101]        -0.2078      0.062     -3.333      0.001      -0.330      -0.086
C(countyfips)[T.8107]        -0.2276      0.063     -3.599      0.000      -0.352      -0.104
C(countyfips)[T.8117]        -0.2925      0.063     -4.659      0.000      -0.416      -0.169
C(countyfips)[T.8123]        -0.1464      0.062     -2.345      0.019      -0.269      -0.024
C(countyfips)[T.9001]        -0.1489      0.063     -2.381      0.017      -0.271      -0.026
C(countyfips)[T.9003]        -0.1992      0.062     -3.187      0.001      -0.322      -0.077
C(countyfips)[T.9005]        -0.0804      0.063     -1.282      0.200      -0.203       0.042
C(countyfips)[T.9007]        -0.1446      0.063     -2.313      0.021      -0.267      -0.022
C(countyfips)[T.9009]        -0.2079      0.063     -3.325      0.001      -0.330      -0.085
C(countyfips)[T.9011]        -0.1479      0.063     -2.364      0.018      -0.271      -0.025
C(countyfips)[T.9013]        -0.1868      0.063     -2.987      0.003      -0.309      -0.064
C(countyfips)[T.10001]       -0.1669      0.063     -2.657      0.008      -0.290      -0.044
C(countyfips)[T.10003]       -0.1944      0.063     -3.100      0.002      -0.317      -0.072
C(countyfips)[T.12001]       -0.2293      0.063     -3.665      0.000      -0.352      -0.107
C(countyfips)[T.12009]       -0.0768      0.063     -1.229      0.219      -0.199       0.046
C(countyfips)[T.12011]       -0.1840      0.063     -2.943      0.003      -0.307      -0.061
C(countyfips)[T.12015]        0.1833      0.062      2.935      0.003       0.061       0.306
C(countyfips)[T.12017]        0.0483      0.062      0.775      0.439      -0.074       0.171
C(countyfips)[T.12019]        0.0224      0.062      0.359      0.720      -0.100       0.145
C(countyfips)[T.12021]        0.1341      0.062      2.145      0.032       0.012       0.257
C(countyfips)[T.12023]       -0.1447      0.062     -2.321      0.020      -0.267      -0.022
C(countyfips)[T.12031]       -0.1628      0.062     -2.608      0.009      -0.285      -0.040
C(countyfips)[T.12033]       -0.1683      0.062     -2.694      0.007      -0.291      -0.046
C(countyfips)[T.12035]        0.1135      0.062      1.818      0.069      -0.009       0.236
C(countyfips)[T.12053]        0.0090      0.062      0.145      0.885      -0.113       0.131
C(countyfips)[T.12055]       -0.0612      0.063     -0.976      0.329      -0.184       0.062
C(countyfips)[T.12057]       -0.1689      0.062     -2.703      0.007      -0.291      -0.046
C(countyfips)[T.12061]        0.0123      0.062      0.197      0.843      -0.110       0.135
C(countyfips)[T.12069]        0.0194      0.062      0.311      0.756      -0.103       0.142
C(countyfips)[T.12071]        0.1512      0.062      2.421      0.015       0.029       0.274
C(countyfips)[T.12073]       -0.2128      0.063     -3.393      0.001      -0.336      -0.090
C(countyfips)[T.12081]        0.0710      0.062      1.136      0.256      -0.051       0.193
C(countyfips)[T.12083]       -0.0243      0.062     -0.389      0.698      -0.147       0.098
C(countyfips)[T.12085]       -0.0165      0.062     -0.264      0.792      -0.139       0.106
C(countyfips)[T.12086]       -0.2348      0.063     -3.752      0.000      -0.358      -0.112
C(countyfips)[T.12087]       -0.0270      0.063     -0.431      0.667      -0.150       0.096
C(countyfips)[T.12091]        0.0003      0.062      0.005      0.996      -0.122       0.123
C(countyfips)[T.12095]       -0.2412      0.063     -3.851      0.000      -0.364      -0.118
C(countyfips)[T.12097]       -0.0325      0.062     -0.520      0.603      -0.155       0.090
C(countyfips)[T.12099]       -0.1087      0.063     -1.738      0.082      -0.231       0.014
C(countyfips)[T.12101]        0.0048      0.062      0.077      0.939      -0.118       0.127
C(countyfips)[T.12103]       -0.1230      0.063     -1.968      0.049      -0.245      -0.000
C(countyfips)[T.12105]       -0.0086      0.062     -0.138      0.890      -0.131       0.114
C(countyfips)[T.12107]       -0.1368      0.063     -2.188      0.029      -0.259      -0.014
C(countyfips)[T.12109]        0.1041      0.062      1.667      0.095      -0.018       0.226
C(countyfips)[T.12111]        0.0148      0.062      0.237      0.813      -0.108       0.137
C(countyfips)[T.12113]       -0.0396      0.062     -0.635      0.525      -0.162       0.083
C(countyfips)[T.12115]        0.1607      0.063      2.570      0.010       0.038       0.283
C(countyfips)[T.12117]       -0.2201      0.063     -3.519      0.000      -0.343      -0.097
C(countyfips)[T.12119]        0.3413      0.062      5.469      0.000       0.219       0.464
C(countyfips)[T.12127]       -0.0382      0.062     -0.612      0.540      -0.161       0.084
C(countyfips)[T.12131]        0.0873      0.063      1.393      0.164      -0.036       0.210
C(countyfips)[T.13013]       -0.1460      0.063     -2.311      0.021      -0.270      -0.022
C(countyfips)[T.13015]       -0.1900      0.063     -3.040      0.002      -0.313      -0.067
C(countyfips)[T.13021]       -0.1660      0.062     -2.661      0.008      -0.288      -0.044
C(countyfips)[T.13031]       -0.1857      0.062     -2.980      0.003      -0.308      -0.064
C(countyfips)[T.13039]       -0.3048      0.063     -4.876      0.000      -0.427      -0.182
C(countyfips)[T.13045]       -0.2111      0.062     -3.379      0.001      -0.334      -0.089
C(countyfips)[T.13051]       -0.2164      0.062     -3.469      0.001      -0.339      -0.094
C(countyfips)[T.13057]       -0.0524      0.062     -0.840      0.401      -0.175       0.070
C(countyfips)[T.13059]       -0.2931      0.063     -4.669      0.000      -0.416      -0.170
C(countyfips)[T.13063]       -0.2253      0.063     -3.589      0.000      -0.348      -0.102
C(countyfips)[T.13067]       -0.1860      0.063     -2.975      0.003      -0.309      -0.063
C(countyfips)[T.13073]       -0.1191      0.063     -1.904      0.057      -0.242       0.003
C(countyfips)[T.13077]       -0.0802      0.062     -1.284      0.199      -0.203       0.042
C(countyfips)[T.13089]       -0.2229      0.063     -3.564      0.000      -0.345      -0.100
C(countyfips)[T.13095]       -0.2152      0.062     -3.452      0.001      -0.337      -0.093
C(countyfips)[T.13097]       -0.2167      0.063     -3.462      0.001      -0.339      -0.094
C(countyfips)[T.13113]       -0.0582      0.062     -0.933      0.351      -0.181       0.064
C(countyfips)[T.13117]       -0.0397      0.063     -0.632      0.528      -0.163       0.083
C(countyfips)[T.13121]       -0.2092      0.063     -3.339      0.001      -0.332      -0.086
C(countyfips)[T.13129]       -0.1660      0.063     -2.642      0.008      -0.289      -0.043
C(countyfips)[T.13135]       -0.1637      0.062     -2.622      0.009      -0.286      -0.041
C(countyfips)[T.13139]       -0.1006      0.062     -1.612      0.107      -0.223       0.022
C(countyfips)[T.13151]       -0.0959      0.062     -1.536      0.124      -0.218       0.026
C(countyfips)[T.13153]       -0.0992      0.062     -1.591      0.112      -0.221       0.023
C(countyfips)[T.13179]       -0.3141      0.063     -4.965      0.000      -0.438      -0.190
C(countyfips)[T.13185]       -0.2129      0.063     -3.395      0.001      -0.336      -0.090
C(countyfips)[T.13215]       -0.2907      0.062     -4.653      0.000      -0.413      -0.168
C(countyfips)[T.13217]       -0.0801      0.062     -1.285      0.199      -0.202       0.042
C(countyfips)[T.13245]       -0.2326      0.063     -3.720      0.000      -0.355      -0.110
C(countyfips)[T.13247]       -0.1606      0.063     -2.557      0.011      -0.284      -0.037
C(countyfips)[T.13275]       -0.1922      0.062     -3.079      0.002      -0.315      -0.070
C(countyfips)[T.13297]       -0.0190      0.062     -0.305      0.760      -0.141       0.103
C(countyfips)[T.13313]       -0.2197      0.063     -3.511      0.000      -0.342      -0.097
C(countyfips)[T.15003]       -0.3040      0.063     -4.814      0.000      -0.428      -0.180
C(countyfips)[T.16001]       -0.1688      0.063     -2.700      0.007      -0.291      -0.046
C(countyfips)[T.16005]       -0.3246      0.062     -5.198      0.000      -0.447      -0.202
C(countyfips)[T.16017]       -0.1045      0.062     -1.673      0.094      -0.227       0.018
C(countyfips)[T.16019]       -0.1526      0.063     -2.441      0.015      -0.275      -0.030
C(countyfips)[T.16027]       -0.0915      0.062     -1.465      0.143      -0.214       0.031
C(countyfips)[T.16055]       -0.0812      0.063     -1.293      0.196      -0.204       0.042
C(countyfips)[T.17031]       -0.2811      0.063     -4.491      0.000      -0.404      -0.158
C(countyfips)[T.17037]       -0.3074      0.063     -4.907      0.000      -0.430      -0.185
C(countyfips)[T.17043]       -0.2212      0.063     -3.531      0.000      -0.344      -0.098
C(countyfips)[T.17089]       -0.1973      0.062     -3.158      0.002      -0.320      -0.075
C(countyfips)[T.17097]       -0.2212      0.062     -3.541      0.000      -0.344      -0.099
C(countyfips)[T.17099]       -0.2935      0.063     -4.680      0.000      -0.416      -0.171
C(countyfips)[T.17111]       -0.1941      0.063     -3.092      0.002      -0.317      -0.071
C(countyfips)[T.17119]       -0.2587      0.063     -4.123      0.000      -0.382      -0.136
C(countyfips)[T.17143]       -0.3277      0.062     -5.251      0.000      -0.450      -0.205
C(countyfips)[T.17163]       -0.2403      0.063     -3.828      0.000      -0.363      -0.117
C(countyfips)[T.17167]       -0.2491      0.063     -3.978      0.000      -0.372      -0.126
C(countyfips)[T.17183]       -0.3182      0.063     -5.064      0.000      -0.441      -0.195
C(countyfips)[T.17197]       -0.1938      0.062     -3.102      0.002      -0.316      -0.071
C(countyfips)[T.17201]       -0.2768      0.063     -4.428      0.000      -0.399      -0.154
C(countyfips)[T.18003]       -0.2991      0.062     -4.788      0.000      -0.421      -0.177
C(countyfips)[T.18011]       -0.1421      0.062     -2.276      0.023      -0.265      -0.020
C(countyfips)[T.18057]       -0.1214      0.063     -1.938      0.053      -0.244       0.001
C(countyfips)[T.18063]       -0.1496      0.063     -2.386      0.017      -0.272      -0.027
C(countyfips)[T.18081]       -0.2196      0.063     -3.482      0.000      -0.343      -0.096
C(countyfips)[T.18091]       -0.2893      0.062     -4.638      0.000      -0.412      -0.167
C(countyfips)[T.18097]       -0.3255      0.062     -5.213      0.000      -0.448      -0.203
C(countyfips)[T.18127]       -0.2716      0.063     -4.337      0.000      -0.394      -0.149
C(countyfips)[T.18163]       -0.2107      0.062     -3.376      0.001      -0.333      -0.088
C(countyfips)[T.19013]       -0.3492      0.062     -5.592      0.000      -0.472      -0.227
C(countyfips)[T.19061]       -0.2780      0.062     -4.460      0.000      -0.400      -0.156
C(countyfips)[T.19113]       -0.3575      0.063     -5.673      0.000      -0.481      -0.234
C(countyfips)[T.19153]       -0.2986      0.062     -4.779      0.000      -0.421      -0.176
C(countyfips)[T.19155]       -0.3519      0.062     -5.634      0.000      -0.474      -0.229
C(countyfips)[T.19163]       -0.3204      0.063     -5.088      0.000      -0.444      -0.197
C(countyfips)[T.19169]       -0.3469      0.063     -5.528      0.000      -0.470      -0.224
C(countyfips)[T.19193]       -0.3115      0.062     -4.988      0.000      -0.434      -0.189
C(countyfips)[T.20045]       -0.2793      0.063     -4.468      0.000      -0.402      -0.157
C(countyfips)[T.20173]       -0.4099      0.063     -6.538      0.000      -0.533      -0.287
C(countyfips)[T.20209]       -0.2968      0.063     -4.729      0.000      -0.420      -0.174
C(countyfips)[T.21015]       -0.1647      0.063     -2.615      0.009      -0.288      -0.041
C(countyfips)[T.21037]       -0.2249      0.063     -3.591      0.000      -0.348      -0.102
C(countyfips)[T.21059]       -0.2159      0.062     -3.457      0.001      -0.338      -0.093
C(countyfips)[T.21067]       -0.2530      0.063     -4.043      0.000      -0.376      -0.130
C(countyfips)[T.21111]       -0.2636      0.063     -4.216      0.000      -0.386      -0.141
C(countyfips)[T.21199]       -0.1182      0.063     -1.885      0.059      -0.241       0.005
C(countyfips)[T.21227]       -0.1774      0.062     -2.841      0.005      -0.300      -0.055
C(countyfips)[T.22005]       -0.1814      0.064     -2.851      0.004      -0.306      -0.057
C(countyfips)[T.22017]       -0.2239      0.062     -3.584      0.000      -0.346      -0.101
C(countyfips)[T.22033]       -0.2318      0.063     -3.709      0.000      -0.354      -0.109
C(countyfips)[T.22051]       -0.2557      0.063     -4.090      0.000      -0.378      -0.133
C(countyfips)[T.22055]       -0.1550      0.062     -2.481      0.013      -0.277      -0.033
C(countyfips)[T.22063]       -0.1370      0.063     -2.192      0.028      -0.260      -0.014
C(countyfips)[T.22071]       -0.2642      0.063     -4.201      0.000      -0.387      -0.141
C(countyfips)[T.22073]       -0.2300      0.062     -3.689      0.000      -0.352      -0.108
C(countyfips)[T.22103]       -0.1013      0.062     -1.621      0.105      -0.224       0.021
C(countyfips)[T.22105]       -0.1182      0.062     -1.893      0.058      -0.241       0.004
C(countyfips)[T.22109]       -0.2768      0.062     -4.436      0.000      -0.399      -0.155
C(countyfips)[T.23001]       -0.2289      0.062     -3.671      0.000      -0.351      -0.107
C(countyfips)[T.23005]       -0.1744      0.062     -2.791      0.005      -0.297      -0.052
C(countyfips)[T.23019]       -0.2505      0.063     -3.968      0.000      -0.374      -0.127
C(countyfips)[T.24001]       -0.1970      0.063     -3.144      0.002      -0.320      -0.074
C(countyfips)[T.24003]       -0.1850      0.062     -2.963      0.003      -0.307      -0.063
C(countyfips)[T.24005]       -0.1868      0.063     -2.989      0.003      -0.309      -0.064
C(countyfips)[T.24009]       -0.1187      0.062     -1.900      0.057      -0.241       0.004
C(countyfips)[T.24013]       -0.1195      0.062     -1.914      0.056      -0.242       0.003
C(countyfips)[T.24017]       -0.1244      0.063     -1.979      0.048      -0.248      -0.001
C(countyfips)[T.24021]       -0.0593      0.062     -0.950      0.342      -0.182       0.063
C(countyfips)[T.24025]       -0.1416      0.062     -2.268      0.023      -0.264      -0.019
C(countyfips)[T.24027]       -0.1601      0.063     -2.554      0.011      -0.283      -0.037
C(countyfips)[T.24031]       -0.2312      0.063     -3.691      0.000      -0.354      -0.108
C(countyfips)[T.24033]       -0.2578      0.063     -4.110      0.000      -0.381      -0.135
C(countyfips)[T.24043]       -0.1980      0.062     -3.172      0.002      -0.320      -0.076
C(countyfips)[T.24510]       -0.3040      0.063     -4.837      0.000      -0.427      -0.181
C(countyfips)[T.25001]       -0.0773      0.062     -1.238      0.216      -0.200       0.045
C(countyfips)[T.25003]       -0.0872      0.063     -1.378      0.168      -0.211       0.037
C(countyfips)[T.25017]       -0.2633      0.063     -4.204      0.000      -0.386      -0.141
C(countyfips)[T.25021]       -0.2037      0.063     -3.255      0.001      -0.326      -0.081
C(countyfips)[T.25023]       -0.1469      0.063     -2.348      0.019      -0.270      -0.024
C(countyfips)[T.25025]       -0.4819      0.063     -7.654      0.000      -0.605      -0.358
C(countyfips)[T.25027]       -0.2002      0.063     -3.198      0.001      -0.323      -0.077
C(countyfips)[T.26045]       -0.2632      0.062     -4.213      0.000      -0.386      -0.141
C(countyfips)[T.26049]       -0.2560      0.062     -4.095      0.000      -0.378      -0.133
C(countyfips)[T.26065]       -0.3180      0.063     -5.051      0.000      -0.441      -0.195
C(countyfips)[T.26077]       -0.3246      0.063     -5.135      0.000      -0.448      -0.201
C(countyfips)[T.26081]       -0.3015      0.063     -4.809      0.000      -0.424      -0.179
C(countyfips)[T.26099]       -0.2275      0.062     -3.642      0.000      -0.350      -0.105
C(countyfips)[T.26121]       -0.2533      0.063     -4.032      0.000      -0.376      -0.130
C(countyfips)[T.26125]       -0.2009      0.063     -3.206      0.001      -0.324      -0.078
C(countyfips)[T.26139]       -0.2312      0.063     -3.699      0.000      -0.354      -0.109
C(countyfips)[T.26145]       -0.2486      0.062     -3.982      0.000      -0.371      -0.126
C(countyfips)[T.26147]       -0.2374      0.062     -3.801      0.000      -0.360      -0.115
C(countyfips)[T.26161]       -0.3282      0.063     -5.242      0.000      -0.451      -0.205
C(countyfips)[T.26163]       -0.2284      0.063     -3.650      0.000      -0.351      -0.106
C(countyfips)[T.27003]       -0.2595      0.062     -4.157      0.000      -0.382      -0.137
C(countyfips)[T.27005]       -0.2833      0.063     -4.479      0.000      -0.407      -0.159
C(countyfips)[T.27013]       -0.6046      0.063     -9.665      0.000      -0.727      -0.482
C(countyfips)[T.27019]       -0.1470      0.063     -2.350      0.019      -0.270      -0.024
C(countyfips)[T.27025]       -0.1623      0.063     -2.595      0.009      -0.285      -0.040
C(countyfips)[T.27035]       -0.1703      0.063     -2.708      0.007      -0.294      -0.047
C(countyfips)[T.27037]       -0.2500      0.063     -3.997      0.000      -0.373      -0.127
C(countyfips)[T.27053]       -0.3448      0.063     -5.514      0.000      -0.467      -0.222
C(countyfips)[T.27109]       -0.2118      0.062     -3.396      0.001      -0.334      -0.090
C(countyfips)[T.27123]       -0.3410      0.063     -5.455      0.000      -0.464      -0.218
C(countyfips)[T.27131]       -0.1766      0.062     -2.833      0.005      -0.299      -0.054
C(countyfips)[T.27137]       -0.2780      0.062     -4.461      0.000      -0.400      -0.156
C(countyfips)[T.27139]       -0.1979      0.063     -3.137      0.002      -0.322      -0.074
C(countyfips)[T.27145]       -0.2466      0.062     -3.948      0.000      -0.369      -0.124
C(countyfips)[T.27163]       -0.1792      0.063     -2.863      0.004      -0.302      -0.057
C(countyfips)[T.27171]       -0.1570      0.062     -2.515      0.012      -0.279      -0.035
C(countyfips)[T.28033]       -0.1017      0.062     -1.629      0.103      -0.224       0.021
C(countyfips)[T.28047]       -0.2135      0.062     -3.417      0.001      -0.336      -0.091
C(countyfips)[T.28049]       -0.2833      0.062     -4.538      0.000      -0.406      -0.161
C(countyfips)[T.28059]       -0.1192      0.063     -1.899      0.058      -0.242       0.004
C(countyfips)[T.28089]       -0.1023      0.062     -1.642      0.101      -0.224       0.020
C(countyfips)[T.28121]       -0.1244      0.063     -1.990      0.047      -0.247      -0.002
C(countyfips)[T.29019]       -0.2440      0.063     -3.875      0.000      -0.367      -0.121
C(countyfips)[T.29021]       -0.2948      0.062     -4.720      0.000      -0.417      -0.172
C(countyfips)[T.29029]       -0.1856      0.063     -2.964      0.003      -0.308      -0.063
C(countyfips)[T.29031]       -0.2531      0.062     -4.050      0.000      -0.376      -0.131
C(countyfips)[T.29047]       -0.1987      0.063     -3.176      0.001      -0.321      -0.076
C(countyfips)[T.29071]       -0.1679      0.062     -2.693      0.007      -0.290      -0.046
C(countyfips)[T.29077]       -0.3715      0.062     -5.944      0.000      -0.494      -0.249
C(countyfips)[T.29095]       -0.2560      0.062     -4.096      0.000      -0.378      -0.133
C(countyfips)[T.29097]       -0.2696      0.062     -4.327      0.000      -0.392      -0.147
C(countyfips)[T.29099]       -0.1570      0.063     -2.493      0.013      -0.281      -0.034
C(countyfips)[T.29145]       -0.2053      0.063     -3.259      0.001      -0.329      -0.082
C(countyfips)[T.29183]       -0.1134      0.062     -1.815      0.069      -0.236       0.009
C(countyfips)[T.29189]       -0.1961      0.063     -3.137      0.002      -0.319      -0.074
C(countyfips)[T.29510]       -0.3557      0.063     -5.675      0.000      -0.479      -0.233
C(countyfips)[T.30029]       -0.0774      0.063     -1.236      0.217      -0.200       0.045
C(countyfips)[T.30049]       -0.1692      0.062     -2.708      0.007      -0.292      -0.047
C(countyfips)[T.30063]       -0.2446      0.062     -3.924      0.000      -0.367      -0.122
C(countyfips)[T.30111]       -0.2856      0.062     -4.580      0.000      -0.408      -0.163
C(countyfips)[T.31019]       -0.3359      0.062     -5.386      0.000      -0.458      -0.214
C(countyfips)[T.31055]       -0.2835      0.062     -4.543      0.000      -0.406      -0.161
C(countyfips)[T.31079]       -0.3900      0.062     -6.260      0.000      -0.512      -0.268
C(countyfips)[T.31109]       -0.3656      0.062     -5.865      0.000      -0.488      -0.243
C(countyfips)[T.31153]       -0.1854      0.063     -2.964      0.003      -0.308      -0.063
C(countyfips)[T.32003]       -0.1630      0.063     -2.605      0.009      -0.286      -0.040
C(countyfips)[T.32005]       -0.1132      0.062     -1.815      0.070      -0.236       0.009
C(countyfips)[T.32031]       -0.1891      0.062     -3.030      0.002      -0.311      -0.067
C(countyfips)[T.32510]       -0.2789      0.062     -4.471      0.000      -0.401      -0.157
C(countyfips)[T.33001]       -0.1987      0.063     -3.172      0.002      -0.321      -0.076
C(countyfips)[T.33003]       -0.1145      0.063     -1.827      0.068      -0.237       0.008
C(countyfips)[T.33005]       -0.2062      0.062     -3.306      0.001      -0.328      -0.084
C(countyfips)[T.33011]       -0.1957      0.063     -3.123      0.002      -0.318      -0.073
C(countyfips)[T.33015]       -0.1425      0.063     -2.278      0.023      -0.265      -0.020
C(countyfips)[T.33017]       -0.1942      0.062     -3.108      0.002      -0.317      -0.072
C(countyfips)[T.34001]       -0.1153      0.063     -1.840      0.066      -0.238       0.008
C(countyfips)[T.34003]       -0.1694      0.063     -2.705      0.007      -0.292      -0.047
C(countyfips)[T.34009]       -0.1175      0.063     -1.853      0.064      -0.242       0.007
C(countyfips)[T.34011]       -0.1866      0.063     -2.981      0.003      -0.309      -0.064
C(countyfips)[T.34015]       -0.1158      0.063     -1.850      0.064      -0.238       0.007
C(countyfips)[T.34017]       -0.3734      0.063     -5.962      0.000      -0.496      -0.251
C(countyfips)[T.34019]       -0.0828      0.062     -1.326      0.185      -0.205       0.040
C(countyfips)[T.34021]       -0.1906      0.063     -3.047      0.002      -0.313      -0.068
C(countyfips)[T.34023]       -0.2052      0.063     -3.278      0.001      -0.328      -0.082
C(countyfips)[T.34025]       -0.1167      0.063     -1.864      0.062      -0.239       0.006
C(countyfips)[T.34027]       -0.1503      0.063     -2.395      0.017      -0.273      -0.027
C(countyfips)[T.34029]       -0.1188      0.062     -1.901      0.057      -0.241       0.004
C(countyfips)[T.34031]       -0.2065      0.063     -3.281      0.001      -0.330      -0.083
C(countyfips)[T.34035]       -0.1324      0.063     -2.117      0.034      -0.255      -0.010
C(countyfips)[T.34037]       -0.0881      0.063     -1.408      0.159      -0.211       0.035
C(countyfips)[T.34039]       -0.2097      0.063     -3.351      0.001      -0.332      -0.087
C(countyfips)[T.35001]       -0.2301      0.063     -3.679      0.000      -0.353      -0.108
C(countyfips)[T.35013]       -0.1527      0.063     -2.442      0.015      -0.275      -0.030
C(countyfips)[T.35045]       -0.2268      0.062     -3.640      0.000      -0.349      -0.105
C(countyfips)[T.35049]       -0.1346      0.063     -2.147      0.032      -0.258      -0.012
C(countyfips)[T.35055]       -0.1560      0.063     -2.480      0.013      -0.279      -0.033
C(countyfips)[T.36009]       -0.2450      0.062     -3.922      0.000      -0.367      -0.123
C(countyfips)[T.36013]       -0.2357      0.063     -3.757      0.000      -0.359      -0.113
C(countyfips)[T.36015]       -0.2575      0.063     -4.119      0.000      -0.380      -0.135
C(countyfips)[T.36019]       -0.2927      0.062     -4.687      0.000      -0.415      -0.170
C(countyfips)[T.36027]       -0.1420      0.063     -2.267      0.023      -0.265      -0.019
C(countyfips)[T.36029]       -0.2409      0.063     -3.838      0.000      -0.364      -0.118
C(countyfips)[T.36035]       -0.2166      0.062     -3.475      0.001      -0.339      -0.094
C(countyfips)[T.36039]       -0.1999      0.063     -3.196      0.001      -0.323      -0.077
C(countyfips)[T.36043]       -0.2212      0.062     -3.540      0.000      -0.344      -0.099
C(countyfips)[T.36045]       -0.4434      0.063     -7.093      0.000      -0.566      -0.321
C(countyfips)[T.36051]       -0.2270      0.063     -3.609      0.000      -0.350      -0.104
C(countyfips)[T.36053]       -0.2108      0.062     -3.380      0.001      -0.333      -0.089
C(countyfips)[T.36055]       -0.2557      0.063     -4.078      0.000      -0.379      -0.133
C(countyfips)[T.36059]       -0.1859      0.063     -2.971      0.003      -0.309      -0.063
C(countyfips)[T.36061]       -0.7166      0.063    -11.358      0.000      -0.840      -0.593
C(countyfips)[T.36063]       -0.2289      0.062     -3.663      0.000      -0.351      -0.106
C(countyfips)[T.36065]       -0.2396      0.063     -3.832      0.000      -0.362      -0.117
C(countyfips)[T.36067]       -0.2537      0.063     -4.057      0.000      -0.376      -0.131
C(countyfips)[T.36069]       -0.2201      0.063     -3.506      0.000      -0.343      -0.097
C(countyfips)[T.36071]       -0.2115      0.063     -3.369      0.001      -0.335      -0.088
C(countyfips)[T.36075]       -0.2624      0.063     -4.186      0.000      -0.385      -0.140
C(countyfips)[T.36077]       -0.2396      0.062     -3.842      0.000      -0.362      -0.117
C(countyfips)[T.36079]       -0.0786      0.063     -1.255      0.209      -0.201       0.044
C(countyfips)[T.36081]       -0.3125      0.063     -4.986      0.000      -0.435      -0.190
C(countyfips)[T.36085]       -0.2114      0.063     -3.369      0.001      -0.334      -0.088
C(countyfips)[T.36087]       -0.2145      0.063     -3.427      0.001      -0.337      -0.092
C(countyfips)[T.36089]       -0.3088      0.063     -4.937      0.000      -0.431      -0.186
C(countyfips)[T.36091]       -0.1561      0.063     -2.495      0.013      -0.279      -0.033
C(countyfips)[T.36093]       -0.1815      0.063     -2.897      0.004      -0.304      -0.059
C(countyfips)[T.36101]       -0.2887      0.063     -4.607      0.000      -0.412      -0.166
C(countyfips)[T.36103]       -0.1563      0.063     -2.499      0.012      -0.279      -0.034
C(countyfips)[T.36105]       -0.1934      0.063     -3.092      0.002      -0.316      -0.071
C(countyfips)[T.36111]       -0.0866      0.063     -1.384      0.166      -0.209       0.036
C(countyfips)[T.36113]       -0.2273      0.062     -3.646      0.000      -0.350      -0.105
C(countyfips)[T.36119]       -0.2022      0.063     -3.233      0.001      -0.325      -0.080
C(countyfips)[T.37001]       -0.1334      0.063     -2.131      0.033      -0.256      -0.011
C(countyfips)[T.37019]        0.1702      0.062      2.731      0.006       0.048       0.292
C(countyfips)[T.37021]       -0.1685      0.063     -2.688      0.007      -0.291      -0.046
C(countyfips)[T.37025]       -0.1115      0.063     -1.782      0.075      -0.234       0.011
C(countyfips)[T.37027]       -0.2484      0.065     -3.850      0.000      -0.375      -0.122
C(countyfips)[T.37031]       -0.1143      0.062     -1.831      0.067      -0.237       0.008
C(countyfips)[T.37035]       -0.1605      0.063     -2.561      0.010      -0.283      -0.038
C(countyfips)[T.37037]       -0.0597      0.063     -0.955      0.339      -0.182       0.063
C(countyfips)[T.37045]       -0.1701      0.063     -2.713      0.007      -0.293      -0.047
C(countyfips)[T.37047]       -0.1709      0.062     -2.738      0.006      -0.293      -0.049
C(countyfips)[T.37049]       -0.2744      0.062     -4.399      0.000      -0.397      -0.152
C(countyfips)[T.37051]       -0.3002      0.063     -4.797      0.000      -0.423      -0.178
C(countyfips)[T.37055]       -0.1332      0.063     -2.105      0.035      -0.257      -0.009
C(countyfips)[T.37057]       -0.1382      0.062     -2.214      0.027      -0.261      -0.016
C(countyfips)[T.37059]       -0.1270      0.063     -2.019      0.043      -0.250      -0.004
C(countyfips)[T.37063]       -0.2174      0.063     -3.468      0.001      -0.340      -0.095
C(countyfips)[T.37067]       -0.1778      0.062     -2.846      0.004      -0.300      -0.055
C(countyfips)[T.37071]       -0.1425      0.063     -2.276      0.023      -0.265      -0.020
C(countyfips)[T.37081]       -0.2394      0.063     -3.829      0.000      -0.362      -0.117
C(countyfips)[T.37085]       -0.1469      0.063     -2.344      0.019      -0.270      -0.024
C(countyfips)[T.37087]       -0.1161      0.063     -1.844      0.065      -0.240       0.007
C(countyfips)[T.37089]       -0.0811      0.062     -1.298      0.194      -0.204       0.041
C(countyfips)[T.37097]       -0.0417      0.062     -0.668      0.504      -0.164       0.081
C(countyfips)[T.37101]       -0.0332      0.062     -0.532      0.595      -0.155       0.089
C(countyfips)[T.37105]        0.2282      0.062      3.654      0.000       0.106       0.351
C(countyfips)[T.37109]       -0.0202      0.062     -0.324      0.746      -0.143       0.102
C(countyfips)[T.37119]       -0.1806      0.062     -2.892      0.004      -0.303      -0.058
C(countyfips)[T.37125]       -0.0567      0.063     -0.907      0.365      -0.179       0.066
C(countyfips)[T.37127]       -0.1589      0.062     -2.542      0.011      -0.281      -0.036
C(countyfips)[T.37129]       -0.1553      0.062     -2.486      0.013      -0.278      -0.033
C(countyfips)[T.37133]       -0.2664      0.063     -4.261      0.000      -0.389      -0.144
C(countyfips)[T.37135]       -0.2065      0.063     -3.291      0.001      -0.329      -0.083
C(countyfips)[T.37139]       -0.1239      0.063     -1.980      0.048      -0.247      -0.001
C(countyfips)[T.37147]       -0.2170      0.062     -3.477      0.001      -0.339      -0.095
C(countyfips)[T.37151]       -0.2370      0.063     -3.791      0.000      -0.360      -0.114
C(countyfips)[T.37155]       -0.1562      0.062     -2.499      0.012      -0.279      -0.034
C(countyfips)[T.37157]       -0.1783      0.062     -2.855      0.004      -0.301      -0.056
C(countyfips)[T.37159]       -0.0870      0.062     -1.395      0.163      -0.209       0.035
C(countyfips)[T.37161]       -0.1586      0.062     -2.537      0.011      -0.281      -0.036
C(countyfips)[T.37163]       -0.1638      0.062     -2.630      0.009      -0.286      -0.042
C(countyfips)[T.37167]       -0.0915      0.062     -1.466      0.143      -0.214       0.031
C(countyfips)[T.37169]       -0.0782      0.062     -1.253      0.210      -0.200       0.044
C(countyfips)[T.37179]       -0.0805      0.062     -1.288      0.198      -0.203       0.042
C(countyfips)[T.37183]       -0.1303      0.062     -2.085      0.037      -0.253      -0.008
C(countyfips)[T.37189]       -0.2508      0.063     -4.006      0.000      -0.374      -0.128
C(countyfips)[T.37191]       -0.2371      0.063     -3.753      0.000      -0.361      -0.113
C(countyfips)[T.37193]       -0.1180      0.062     -1.891      0.059      -0.240       0.004
C(countyfips)[T.37195]       -0.1884      0.062     -3.018      0.003      -0.311      -0.066
C(countyfips)[T.38017]       -0.4859      0.062     -7.782      0.000      -0.608      -0.364
C(countyfips)[T.38035]       -0.5034      0.063     -8.031      0.000      -0.626      -0.381
C(countyfips)[T.39017]       -0.2077      0.062     -3.327      0.001      -0.330      -0.085
C(countyfips)[T.39025]       -0.1415      0.062     -2.269      0.023      -0.264      -0.019
C(countyfips)[T.39035]       -0.2213      0.063     -3.538      0.000      -0.344      -0.099
C(countyfips)[T.39041]       -0.0564      0.062     -0.904      0.366      -0.179       0.066
C(countyfips)[T.39043]       -0.2925      0.062     -4.683      0.000      -0.415      -0.170
C(countyfips)[T.39045]       -0.1391      0.063     -2.224      0.026      -0.262      -0.017
C(countyfips)[T.39049]       -0.2858      0.062     -4.573      0.000      -0.408      -0.163
C(countyfips)[T.39055]       -0.1422      0.062     -2.281      0.023      -0.264      -0.020
C(countyfips)[T.39057]       -0.1934      0.062     -3.095      0.002      -0.316      -0.071
C(countyfips)[T.39061]       -0.2351      0.062     -3.763      0.000      -0.358      -0.113
C(countyfips)[T.39085]       -0.1656      0.062     -2.651      0.008      -0.288      -0.043
C(countyfips)[T.39089]       -0.1802      0.062     -2.886      0.004      -0.303      -0.058
C(countyfips)[T.39093]       -0.1682      0.062     -2.692      0.007      -0.291      -0.046
C(countyfips)[T.39095]       -0.2451      0.062     -3.924      0.000      -0.368      -0.123
C(countyfips)[T.39099]       -0.1952      0.063     -3.123      0.002      -0.318      -0.073
C(countyfips)[T.39103]       -0.1644      0.063     -2.623      0.009      -0.287      -0.042
C(countyfips)[T.39109]       -0.1471      0.063     -2.351      0.019      -0.270      -0.024
C(countyfips)[T.39113]       -0.2022      0.063     -3.235      0.001      -0.325      -0.080
C(countyfips)[T.39119]       -0.2445      0.064     -3.792      0.000      -0.371      -0.118
C(countyfips)[T.39123]       -0.3429      0.064     -5.399      0.000      -0.467      -0.218
C(countyfips)[T.39133]       -0.2070      0.063     -3.309      0.001      -0.330      -0.084
C(countyfips)[T.39147]       -0.2979      0.063     -4.740      0.000      -0.421      -0.175
C(countyfips)[T.39151]       -0.1720      0.063     -2.747      0.006      -0.295      -0.049
C(countyfips)[T.39153]       -0.1950      0.063     -3.120      0.002      -0.318      -0.073
C(countyfips)[T.39155]       -0.2025      0.063     -3.232      0.001      -0.325      -0.080
C(countyfips)[T.39157]       -0.2236      0.062     -3.579      0.000      -0.346      -0.101
C(countyfips)[T.39165]       -0.1069      0.062     -1.712      0.087      -0.229       0.016
C(countyfips)[T.39169]       -0.1844      0.063     -2.948      0.003      -0.307      -0.062
C(countyfips)[T.40031]       -0.2100      0.062     -3.362      0.001      -0.332      -0.088
C(countyfips)[T.40119]       -0.3619      0.062     -5.802      0.000      -0.484      -0.240
C(countyfips)[T.40143]       -0.2380      0.063     -3.806      0.000      -0.361      -0.115
C(countyfips)[T.41005]       -0.1919      0.062     -3.075      0.002      -0.314      -0.070
C(countyfips)[T.41007]       -0.2865      0.063     -4.564      0.000      -0.410      -0.163
C(countyfips)[T.41011]       -0.2430      0.063     -3.865      0.000      -0.366      -0.120
C(countyfips)[T.41017]       -0.1107      0.062     -1.773      0.076      -0.233       0.012
C(countyfips)[T.41019]       -0.1649      0.062     -2.645      0.008      -0.287      -0.043
C(countyfips)[T.41029]       -0.2290      0.063     -3.662      0.000      -0.352      -0.106
C(countyfips)[T.41033]       -0.1259      0.062     -2.017      0.044      -0.248      -0.004
C(countyfips)[T.41035]       -0.1371      0.063     -2.190      0.029      -0.260      -0.014
C(countyfips)[T.41039]       -0.2578      0.062     -4.128      0.000      -0.380      -0.135
C(countyfips)[T.41041]       -0.2566      0.063     -4.097      0.000      -0.379      -0.134
C(countyfips)[T.41043]       -0.1596      0.062     -2.558      0.011      -0.282      -0.037
C(countyfips)[T.41047]       -0.4008      0.063     -6.410      0.000      -0.523      -0.278
C(countyfips)[T.41051]       -0.3398      0.063     -5.420      0.000      -0.463      -0.217
C(countyfips)[T.41059]       -0.3268      0.063     -5.189      0.000      -0.450      -0.203
C(countyfips)[T.41067]       -0.1957      0.063     -3.131      0.002      -0.318      -0.073
C(countyfips)[T.42003]       -0.2726      0.063     -4.361      0.000      -0.395      -0.150
C(countyfips)[T.42007]       -0.2240      0.063     -3.583      0.000      -0.347      -0.101
C(countyfips)[T.42011]       -0.2146      0.063     -3.430      0.001      -0.337      -0.092
C(countyfips)[T.42013]       -0.1908      0.062     -3.055      0.002      -0.313      -0.068
C(countyfips)[T.42015]       -0.2379      0.062     -3.813      0.000      -0.360      -0.116
C(countyfips)[T.42017]       -0.1662      0.063     -2.657      0.008      -0.289      -0.044
C(countyfips)[T.42019]       -0.1770      0.062     -2.833      0.005      -0.299      -0.055
C(countyfips)[T.42021]       -0.2121      0.063     -3.388      0.001      -0.335      -0.089
C(countyfips)[T.42027]       -0.2515      0.063     -4.009      0.000      -0.374      -0.129
C(countyfips)[T.42029]       -0.1518      0.063     -2.426      0.015      -0.274      -0.029
C(countyfips)[T.42033]       -0.2384      0.063     -3.814      0.000      -0.361      -0.116
C(countyfips)[T.42041]       -0.1633      0.063     -2.612      0.009      -0.286      -0.041
C(countyfips)[T.42043]       -0.2370      0.063     -3.787      0.000      -0.360      -0.114
C(countyfips)[T.42045]       -0.2116      0.063     -3.383      0.001      -0.334      -0.089
C(countyfips)[T.42049]       -0.2555      0.063     -4.086      0.000      -0.378      -0.133
C(countyfips)[T.42051]       -0.2118      0.063     -3.379      0.001      -0.335      -0.089
C(countyfips)[T.42055]       -0.1753      0.063     -2.797      0.005      -0.298      -0.052
C(countyfips)[T.42063]       -0.1943      0.063     -3.100      0.002      -0.317      -0.071
C(countyfips)[T.42065]       -0.2156      0.062     -3.453      0.001      -0.338      -0.093
C(countyfips)[T.42069]       -0.2184      0.062     -3.497      0.000      -0.341      -0.096
C(countyfips)[T.42071]       -0.2237      0.063     -3.578      0.000      -0.346      -0.101
C(countyfips)[T.42073]       -0.2097      0.062     -3.362      0.001      -0.332      -0.087
C(countyfips)[T.42075]       -0.1906      0.063     -3.044      0.002      -0.313      -0.068
C(countyfips)[T.42077]       -0.1972      0.062     -3.158      0.002      -0.320      -0.075
C(countyfips)[T.42079]       -0.1687      0.063     -2.696      0.007      -0.291      -0.046
C(countyfips)[T.42085]       -0.3024      0.063     -4.772      0.000      -0.427      -0.178
C(countyfips)[T.42089]       -0.2324      0.063     -3.716      0.000      -0.355      -0.110
C(countyfips)[T.42091]       -0.1463      0.062     -2.341      0.019      -0.269      -0.024
C(countyfips)[T.42095]       -0.1896      0.063     -3.028      0.002      -0.312      -0.067
C(countyfips)[T.42097]       -0.2010      0.063     -3.216      0.001      -0.324      -0.078
C(countyfips)[T.42103]       -0.1387      0.062     -2.221      0.026      -0.261      -0.016
C(countyfips)[T.42115]       -0.2701      0.063     -4.315      0.000      -0.393      -0.147
C(countyfips)[T.42125]       -0.1667      0.062     -2.670      0.008      -0.289      -0.044
C(countyfips)[T.42129]       -0.2145      0.063     -3.423      0.001      -0.337      -0.092
C(countyfips)[T.42133]       -0.2009      0.063     -3.210      0.001      -0.324      -0.078
C(countyfips)[T.44003]       -0.1238      0.063     -1.970      0.049      -0.247      -0.001
C(countyfips)[T.44007]       -0.2282      0.063     -3.647      0.000      -0.351      -0.106
C(countyfips)[T.44009]       -0.1065      0.062     -1.708      0.088      -0.229       0.016
C(countyfips)[T.45003]       -0.1075      0.062     -1.720      0.085      -0.230       0.015
C(countyfips)[T.45007]       -0.1364      0.063     -2.174      0.030      -0.259      -0.013
C(countyfips)[T.45015]       -0.0839      0.062     -1.345      0.179      -0.206       0.038
C(countyfips)[T.45019]       -0.1682      0.062     -2.696      0.007      -0.290      -0.046
C(countyfips)[T.45035]       -0.1266      0.062     -2.028      0.043      -0.249      -0.004
C(countyfips)[T.45043]       -0.0403      0.063     -0.643      0.520      -0.163       0.083
C(countyfips)[T.45045]       -0.1220      0.063     -1.951      0.051      -0.245       0.001
C(countyfips)[T.45051]        0.0256      0.063      0.410      0.682      -0.097       0.148
C(countyfips)[T.45057]        0.0707      0.062      1.133      0.257      -0.052       0.193
C(countyfips)[T.45063]       -0.1269      0.062     -2.031      0.042      -0.249      -0.004
C(countyfips)[T.45077]       -0.1680      0.063     -2.679      0.007      -0.291      -0.045
C(countyfips)[T.45079]       -0.2066      0.063     -3.302      0.001      -0.329      -0.084
C(countyfips)[T.45083]       -0.1425      0.062     -2.283      0.022      -0.265      -0.020
C(countyfips)[T.45085]       -0.1999      0.062     -3.203      0.001      -0.322      -0.078
C(countyfips)[T.45091]       -0.1023      0.062     -1.640      0.101      -0.225       0.020
C(countyfips)[T.46099]       -0.2961      0.062     -4.751      0.000      -0.418      -0.174
C(countyfips)[T.46103]       -0.1467      0.063     -2.329      0.020      -0.270      -0.023
C(countyfips)[T.47001]       -0.1141      0.062     -1.829      0.067      -0.236       0.008
C(countyfips)[T.47009]       -0.1046      0.063     -1.666      0.096      -0.228       0.018
C(countyfips)[T.47011]       -0.1531      0.063     -2.446      0.014      -0.276      -0.030
C(countyfips)[T.47037]       -0.3092      0.062     -4.951      0.000      -0.432      -0.187
C(countyfips)[T.47043]       -0.0984      0.062     -1.578      0.115      -0.221       0.024
C(countyfips)[T.47065]       -0.1855      0.063     -2.961      0.003      -0.308      -0.063
C(countyfips)[T.47093]       -0.1571      0.063     -2.512      0.012      -0.280      -0.034
C(countyfips)[T.47113]       -0.1464      0.063     -2.342      0.019      -0.269      -0.024
C(countyfips)[T.47141]       -0.1081      0.063     -1.725      0.085      -0.231       0.015
C(countyfips)[T.47149]       -0.1456      0.062     -2.336      0.019      -0.268      -0.023
C(countyfips)[T.47155]       -0.2071      0.063     -3.289      0.001      -0.331      -0.084
C(countyfips)[T.47157]       -0.2078      0.063     -3.320      0.001      -0.330      -0.085
C(countyfips)[T.47163]       -0.1094      0.062     -1.755      0.079      -0.232       0.013
C(countyfips)[T.47165]       -0.1125      0.062     -1.805      0.071      -0.235       0.010
C(countyfips)[T.47179]       -0.1582      0.063     -2.531      0.011      -0.281      -0.036
C(countyfips)[T.47187]       -0.0490      0.062     -0.784      0.433      -0.171       0.073
C(countyfips)[T.47189]       -0.0158      0.062     -0.254      0.800      -0.138       0.106
C(countyfips)[T.48013]       -0.0743      0.062     -1.189      0.234      -0.197       0.048
C(countyfips)[T.48021]       -0.0130      0.062     -0.208      0.835      -0.135       0.109
C(countyfips)[T.48027]       -0.2447      0.063     -3.887      0.000      -0.368      -0.121
C(countyfips)[T.48029]       -0.1971      0.063     -3.149      0.002      -0.320      -0.074
C(countyfips)[T.48039]       -0.1686      0.063     -2.693      0.007      -0.291      -0.046
C(countyfips)[T.48041]       -0.2779      0.062     -4.452      0.000      -0.400      -0.156
C(countyfips)[T.48061]       -0.0649      0.062     -1.040      0.298      -0.187       0.057
C(countyfips)[T.48085]       -0.0561      0.063     -0.894      0.372      -0.179       0.067
C(countyfips)[T.48091]        0.1217      0.062      1.954      0.051      -0.000       0.244
C(countyfips)[T.48113]       -0.2482      0.063     -3.969      0.000      -0.371      -0.126
C(countyfips)[T.48121]       -0.0846      0.062     -1.354      0.176      -0.207       0.038
C(countyfips)[T.48139]       -0.0134      0.062     -0.215      0.830      -0.136       0.109
C(countyfips)[T.48141]       -0.1978      0.062     -3.168      0.002      -0.320      -0.075
C(countyfips)[T.48157]       -0.0721      0.063     -1.149      0.250      -0.195       0.051
C(countyfips)[T.48167]       -0.1896      0.063     -3.032      0.002      -0.312      -0.067
C(countyfips)[T.48171]       -0.0852      0.063     -1.361      0.173      -0.208       0.038
C(countyfips)[T.48181]       -0.0831      0.062     -1.333      0.183      -0.205       0.039
C(countyfips)[T.48183]       -0.2074      0.063     -3.317      0.001      -0.330      -0.085
C(countyfips)[T.48187]       -0.0965      0.062     -1.547      0.122      -0.219       0.026
C(countyfips)[T.48201]       -0.2027      0.063     -3.242      0.001      -0.325      -0.080
C(countyfips)[T.48209]       -0.0590      0.063     -0.942      0.346      -0.182       0.064
C(countyfips)[T.48215]       -0.1034      0.062     -1.654      0.098      -0.226       0.019
C(countyfips)[T.48221]       -0.0184      0.063     -0.293      0.769      -0.141       0.105
C(countyfips)[T.48231]       -0.1060      0.063     -1.694      0.090      -0.229       0.017
C(countyfips)[T.48245]       -0.2625      0.063     -4.191      0.000      -0.385      -0.140
C(countyfips)[T.48251]       -0.0355      0.062     -0.568      0.570      -0.158       0.087
C(countyfips)[T.48257]        0.1743      0.062      2.795      0.005       0.052       0.297
C(countyfips)[T.48265]       -0.1827      0.063     -2.911      0.004      -0.306      -0.060
C(countyfips)[T.48291]       -0.0312      0.062     -0.499      0.618      -0.154       0.091
C(countyfips)[T.48303]       -0.2330      0.062     -3.738      0.000      -0.355      -0.111
C(countyfips)[T.48309]       -0.1690      0.062     -2.709      0.007      -0.291      -0.047
C(countyfips)[T.48329]       -0.3940      0.063     -6.269      0.000      -0.517      -0.271
C(countyfips)[T.48339]       -0.0331      0.062     -0.530      0.596      -0.156       0.089
C(countyfips)[T.48355]       -0.1946      0.062     -3.118      0.002      -0.317      -0.072
C(countyfips)[T.48367]        0.0260      0.063      0.413      0.680      -0.097       0.149
C(countyfips)[T.48375]       -0.2348      0.062     -3.761      0.000      -0.357      -0.112
C(countyfips)[T.48381]       -0.2153      0.062     -3.447      0.001      -0.338      -0.093
C(countyfips)[T.48397]        0.1113      0.062      1.785      0.074      -0.011       0.233
C(countyfips)[T.48423]       -0.1279      0.062     -2.046      0.041      -0.250      -0.005
C(countyfips)[T.48439]       -0.2042      0.063     -3.264      0.001      -0.327      -0.082
C(countyfips)[T.48451]       -0.2655      0.062     -4.258      0.000      -0.388      -0.143
C(countyfips)[T.48453]       -0.2353      0.063     -3.753      0.000      -0.358      -0.112
C(countyfips)[T.48469]       -0.2237      0.063     -3.571      0.000      -0.346      -0.101
C(countyfips)[T.48471]       -0.1727      0.062     -2.769      0.006      -0.295      -0.050
C(countyfips)[T.48479]       -0.1890      0.063     -3.008      0.003      -0.312      -0.066
C(countyfips)[T.48485]       -0.8925      0.062    -14.314      0.000      -1.015      -0.770
C(countyfips)[T.48491]        0.0145      0.063      0.232      0.817      -0.108       0.137
C(countyfips)[T.49005]       -0.4490      0.062     -7.197      0.000      -0.571      -0.327
C(countyfips)[T.49035]       -0.2801      0.063     -4.480      0.000      -0.403      -0.158
C(countyfips)[T.49043]       -0.0172      0.063     -0.275      0.783      -0.140       0.106
C(countyfips)[T.49045]       -0.1052      0.063     -1.677      0.094      -0.228       0.018
C(countyfips)[T.49049]       -0.1871      0.063     -2.991      0.003      -0.310      -0.064
C(countyfips)[T.49057]       -0.2046      0.063     -3.272      0.001      -0.327      -0.082
C(countyfips)[T.50021]       -0.1765      0.063     -2.817      0.005      -0.299      -0.054
C(countyfips)[T.50025]       -0.1237      0.062     -1.982      0.048      -0.246      -0.001
C(countyfips)[T.51003]       -0.1668      0.063     -2.667      0.008      -0.289      -0.044
C(countyfips)[T.51013]       -0.4636      0.063     -7.361      0.000      -0.587      -0.340
C(countyfips)[T.51015]       -0.2183      0.063     -3.491      0.000      -0.341      -0.096
C(countyfips)[T.51019]       -0.1436      0.063     -2.297      0.022      -0.266      -0.021
C(countyfips)[T.51041]       -0.1140      0.063     -1.824      0.068      -0.237       0.009
C(countyfips)[T.51047]       -0.0712      0.063     -1.137      0.256      -0.194       0.052
C(countyfips)[T.51059]       -0.2357      0.063     -3.766      0.000      -0.358      -0.113
C(countyfips)[T.51061]       -0.1480      0.062     -2.368      0.018      -0.270      -0.025
C(countyfips)[T.51069]       -0.1391      0.063     -2.221      0.026      -0.262      -0.016
C(countyfips)[T.51085]       -0.0920      0.063     -1.471      0.141      -0.215       0.031
C(countyfips)[T.51087]       -0.1914      0.063     -3.050      0.002      -0.314      -0.068
C(countyfips)[T.51095]       -0.0901      0.063     -1.441      0.149      -0.213       0.032
C(countyfips)[T.51107]       -0.1105      0.062     -1.769      0.077      -0.233       0.012
C(countyfips)[T.51121]       -0.3591      0.063     -5.740      0.000      -0.482      -0.236
C(countyfips)[T.51153]       -0.2232      0.062     -3.571      0.000      -0.346      -0.101
C(countyfips)[T.51161]       -0.1368      0.062     -2.191      0.028      -0.259      -0.014
C(countyfips)[T.51177]       -0.0760      0.063     -1.214      0.225      -0.199       0.047
C(countyfips)[T.51179]       -0.0988      0.062     -1.584      0.113      -0.221       0.023
C(countyfips)[T.51199]       -0.1423      0.062     -2.280      0.023      -0.265      -0.020
C(countyfips)[T.51510]       -0.3601      0.063     -5.761      0.000      -0.483      -0.238
C(countyfips)[T.51550]       -0.1724      0.063     -2.757      0.006      -0.295      -0.050
C(countyfips)[T.51630]       -0.1913      0.063     -3.050      0.002      -0.314      -0.068
C(countyfips)[T.51650]       -0.1904      0.063     -3.027      0.002      -0.314      -0.067
C(countyfips)[T.51683]       -0.2295      0.062     -3.680      0.000      -0.352      -0.107
C(countyfips)[T.51700]       -0.2731      0.062     -4.374      0.000      -0.396      -0.151
C(countyfips)[T.51710]       -0.3237      0.062     -5.185      0.000      -0.446      -0.201
C(countyfips)[T.51740]       -0.2304      0.063     -3.686      0.000      -0.353      -0.108
C(countyfips)[T.51800]       -0.0709      0.063     -1.132      0.258      -0.194       0.052
C(countyfips)[T.51810]       -0.2399      0.063     -3.832      0.000      -0.363      -0.117
C(countyfips)[T.51840]       -0.3635      0.063     -5.813      0.000      -0.486      -0.241
C(countyfips)[T.53005]       -0.2097      0.063     -3.333      0.001      -0.333      -0.086
C(countyfips)[T.53007]       -0.1930      0.063     -3.081      0.002      -0.316      -0.070
C(countyfips)[T.53015]       -0.2219      0.063     -3.534      0.000      -0.345      -0.099
C(countyfips)[T.53025]       -0.1777      0.062     -2.845      0.004      -0.300      -0.055
C(countyfips)[T.53033]       -0.2946      0.063     -4.703      0.000      -0.417      -0.172
C(countyfips)[T.53035]       -0.2878      0.063     -4.595      0.000      -0.411      -0.165
C(countyfips)[T.53041]       -0.1295      0.062     -2.078      0.038      -0.252      -0.007
C(countyfips)[T.53053]       -0.2435      0.063     -3.895      0.000      -0.366      -0.121
C(countyfips)[T.53057]       -0.1964      0.062     -3.150      0.002      -0.319      -0.074
C(countyfips)[T.53061]       -0.1962      0.063     -3.132      0.002      -0.319      -0.073
C(countyfips)[T.53063]       -0.1929      0.062     -3.093      0.002      -0.315      -0.071
C(countyfips)[T.53067]       -0.1817      0.063     -2.902      0.004      -0.304      -0.059
C(countyfips)[T.53073]       -0.2191      0.063     -3.504      0.000      -0.342      -0.097
C(countyfips)[T.54003]       -0.0734      0.063     -1.173      0.241      -0.196       0.049
C(countyfips)[T.54011]       -0.2909      0.062     -4.654      0.000      -0.413      -0.168
C(countyfips)[T.54039]       -0.2394      0.063     -3.813      0.000      -0.363      -0.116
C(countyfips)[T.54061]       -0.3653      0.063     -5.836      0.000      -0.488      -0.243
C(countyfips)[T.55009]       -0.3415      0.063     -5.457      0.000      -0.464      -0.219
C(countyfips)[T.55021]       -0.2059      0.062     -3.298      0.001      -0.328      -0.084
C(countyfips)[T.55025]       -0.2957      0.063     -4.726      0.000      -0.418      -0.173
C(countyfips)[T.55031]       -0.2026      0.063     -3.228      0.001      -0.326      -0.080
C(countyfips)[T.55035]       -0.3222      0.062     -5.162      0.000      -0.445      -0.200
C(countyfips)[T.55039]       -0.2438      0.062     -3.912      0.000      -0.366      -0.122
C(countyfips)[T.55059]       -0.2799      0.062     -4.484      0.000      -0.402      -0.158
C(countyfips)[T.55063]       -0.3319      0.062     -5.315      0.000      -0.454      -0.210
C(countyfips)[T.55073]       -0.2270      0.062     -3.634      0.000      -0.349      -0.105
C(countyfips)[T.55079]       -0.3244      0.063     -5.187      0.000      -0.447      -0.202
C(countyfips)[T.55087]       -0.2558      0.063     -4.093      0.000      -0.378      -0.133
C(countyfips)[T.55089]       -0.1371      0.063     -2.192      0.028      -0.260      -0.014
C(countyfips)[T.55095]       -0.2549      0.063     -4.028      0.000      -0.379      -0.131
C(countyfips)[T.55097]       -0.2864      0.062     -4.592      0.000      -0.409      -0.164
C(countyfips)[T.55101]       -0.2398      0.063     -3.833      0.000      -0.362      -0.117
C(countyfips)[T.55111]       -0.2617      0.063     -4.181      0.000      -0.384      -0.139
C(countyfips)[T.55117]       -0.3221      0.063     -5.142      0.000      -0.445      -0.199
C(countyfips)[T.55127]       -0.2751      0.063     -4.394      0.000      -0.398      -0.152
C(countyfips)[T.55131]       -0.2230      0.063     -3.562      0.000      -0.346      -0.100
C(countyfips)[T.55133]       -0.1516      0.062     -2.429      0.015      -0.274      -0.029
C(countyfips)[T.55139]       -0.2760      0.063     -4.397      0.000      -0.399      -0.153
C(countyfips)[T.56021]       -0.2088      0.062     -3.344      0.001      -0.331      -0.086
C(countyfips)[T.56025]       -0.1646      0.062     -2.640      0.008      -0.287      -0.042
C(month)[T.2.0]              -0.0282      0.008     -3.467      0.001      -0.044      -0.012
C(month)[T.3.0]              -0.0258      0.009     -2.801      0.005      -0.044      -0.008
C(month)[T.4.0]              -0.0133      0.009     -1.427      0.153      -0.032       0.005
C(month)[T.5.0]              -0.0066      0.009     -0.715      0.474      -0.025       0.011
C(month)[T.6.0]              -0.0122      0.009     -1.291      0.197      -0.031       0.006
C(month)[T.7.0]              -0.0318      0.010     -3.341      0.001      -0.050      -0.013
C(month)[T.8.0]              -0.0315      0.009     -3.348      0.001      -0.050      -0.013
C(month)[T.9.0]              -0.0337      0.009     -3.679      0.000      -0.052      -0.016
C(month)[T.10.0]             -0.0524      0.009     -5.789      0.000      -0.070      -0.035
C(month)[T.11.0]             -0.0350      0.009     -3.926      0.000      -0.052      -0.018
C(month)[T.12.0]             -0.0206      0.009     -2.319      0.020      -0.038      -0.003
spend_all                    -0.0012      0.000     -6.261      0.000      -0.002      -0.001
gps_retail_and_recreation     0.0017      0.000      8.767      0.000       0.001       0.002
emp                          -0.0014      0.000     -4.587      0.000      -0.002      -0.001
revenue_all                  -0.0004   8.21e-05     -4.914      0.000      -0.001      -0.000
==============================================================================
Omnibus:                     6169.899   Durbin-Watson:                   0.600
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          2257769.413
Skew:                          -0.470   Prob(JB):                         0.00
Kurtosis:                      60.605   Cond. No.                     2.48e+04
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.48e+04. This might indicate that there are
strong multicollinearity or other numerical problems.

The results of this model show that the coefficients on the economic variables are each significant at the 1% level. The correlations are negative except for the foot traffic variable, which has a positive correlation. The model has a low adjusted R-squared, so these results should only be interpreted as representing the average county.

Given the correlation of data within a county, another version of this model uses standard errors that are clustered by county:

In [38]:
ols_formula_fe = 'net_flow_pop ~ spend_all + gps_retail_and_recreation + emp + revenue_all + C(countyfips) + C(month)'

ols_model = smf.ols(ols_formula_fe, data=df_nonmissing).fit(cov_type='cluster', cov_kwds={'groups': df_nonmissing['countyfips']})
print(ols_model.summary())
C:\Users\nloreedwards\Anaconda3\lib\site-packages\statsmodels\base\model.py:1871: ValueWarning:

covariance of constraints does not have full rank. The number of constraints is 667, but rank is 15

                            OLS Regression Results                            
==============================================================================
Dep. Variable:           net_flow_pop   R-squared:                       0.211
Model:                            OLS   Adj. R-squared:                  0.177
Method:                 Least Squares   F-statistic:                     485.4
Date:                Sat, 17 Dec 2022   Prob (F-statistic):               0.00
Time:                        19:56:22   Log-Likelihood:                 1880.1
No. Observations:               16325   AIC:                            -2424.
Df Residuals:                   15657   BIC:                             2720.
Df Model:                         667                                         
Covariance Type:              cluster                                         
=============================================================================================
                                coef    std err          z      P>|z|      [0.025      0.975]
---------------------------------------------------------------------------------------------
Intercept                     0.2097      0.011     18.619      0.000       0.188       0.232
C(countyfips)[T.1055]        -0.1834      0.007    -27.496      0.000      -0.197      -0.170
C(countyfips)[T.1069]        -0.1856      0.007    -25.302      0.000      -0.200      -0.171
C(countyfips)[T.1073]        -0.2197      0.008    -27.536      0.000      -0.235      -0.204
C(countyfips)[T.1081]        -0.2225      0.003    -79.193      0.000      -0.228      -0.217
C(countyfips)[T.1089]        -0.1465      0.004    -32.912      0.000      -0.155      -0.138
C(countyfips)[T.1095]        -0.2127      0.010    -20.933      0.000      -0.233      -0.193
C(countyfips)[T.1097]        -0.1829      0.004    -49.751      0.000      -0.190      -0.176
C(countyfips)[T.1101]        -0.2600      0.006    -43.583      0.000      -0.272      -0.248
C(countyfips)[T.1115]        -0.1195      0.011    -11.307      0.000      -0.140      -0.099
C(countyfips)[T.1117]        -0.1320      0.010    -13.057      0.000      -0.152      -0.112
C(countyfips)[T.1125]        -0.2475      0.004    -58.878      0.000      -0.256      -0.239
C(countyfips)[T.2020]        -0.2756      0.006    -47.925      0.000      -0.287      -0.264
C(countyfips)[T.2090]        -0.3461      0.008    -44.095      0.000      -0.361      -0.331
C(countyfips)[T.4005]        -0.2902      0.005    -59.665      0.000      -0.300      -0.281
C(countyfips)[T.4013]        -0.1268      0.005    -23.509      0.000      -0.137      -0.116
C(countyfips)[T.4015]         0.0357      0.003     12.291      0.000       0.030       0.041
C(countyfips)[T.4017]        -0.0676      0.005    -12.701      0.000      -0.078      -0.057
C(countyfips)[T.4019]        -0.1466      0.005    -29.421      0.000      -0.156      -0.137
C(countyfips)[T.4021]         0.0871      0.003     27.200      0.000       0.081       0.093
C(countyfips)[T.4025]        -0.0629      0.004    -14.971      0.000      -0.071      -0.055
C(countyfips)[T.5031]        -0.3051      0.004    -73.773      0.000      -0.313      -0.297
C(countyfips)[T.5045]        -0.1814      0.006    -30.761      0.000      -0.193      -0.170
C(countyfips)[T.5051]        -0.2637      0.011    -24.564      0.000      -0.285      -0.243
C(countyfips)[T.5143]        -0.2198      0.004    -53.837      0.000      -0.228      -0.212
C(countyfips)[T.6001]        -0.2971      0.008    -39.211      0.000      -0.312      -0.282
C(countyfips)[T.6007]        -0.2810      0.005    -57.984      0.000      -0.291      -0.272
C(countyfips)[T.6013]        -0.2070      0.006    -32.305      0.000      -0.220      -0.194
C(countyfips)[T.6017]        -0.1322      0.008    -15.785      0.000      -0.149      -0.116
C(countyfips)[T.6019]        -0.2213      0.007    -30.916      0.000      -0.235      -0.207
C(countyfips)[T.6023]        -0.2838      0.008    -34.155      0.000      -0.300      -0.268
C(countyfips)[T.6029]        -0.2130      0.006    -35.071      0.000      -0.225      -0.201
C(countyfips)[T.6037]        -0.2723      0.006    -42.741      0.000      -0.285      -0.260
C(countyfips)[T.6039]        -0.1491      0.005    -28.299      0.000      -0.159      -0.139
C(countyfips)[T.6041]        -0.2086      0.010    -20.579      0.000      -0.229      -0.189
C(countyfips)[T.6045]        -0.3139      0.008    -41.224      0.000      -0.329      -0.299
C(countyfips)[T.6047]        -0.2278      0.011    -21.202      0.000      -0.249      -0.207
C(countyfips)[T.6053]        -0.2366      0.009    -26.850      0.000      -0.254      -0.219
C(countyfips)[T.6059]        -0.2006      0.006    -32.659      0.000      -0.213      -0.189
C(countyfips)[T.6061]        -0.1178      0.007    -17.514      0.000      -0.131      -0.105
C(countyfips)[T.6065]        -0.1349      0.007    -18.655      0.000      -0.149      -0.121
C(countyfips)[T.6067]        -0.2210      0.005    -41.007      0.000      -0.232      -0.210
C(countyfips)[T.6069]        -0.1585      0.013    -12.658      0.000      -0.183      -0.134
C(countyfips)[T.6071]        -0.1898      0.005    -39.095      0.000      -0.199      -0.180
C(countyfips)[T.6073]        -0.2298      0.006    -37.021      0.000      -0.242      -0.218
C(countyfips)[T.6075]        -0.5765      0.011    -50.722      0.000      -0.599      -0.554
C(countyfips)[T.6077]        -0.1735      0.007    -24.816      0.000      -0.187      -0.160
C(countyfips)[T.6081]        -0.3286      0.009    -37.211      0.000      -0.346      -0.311
C(countyfips)[T.6083]        -0.2203      0.006    -35.109      0.000      -0.233      -0.208
C(countyfips)[T.6085]        -0.2895      0.007    -39.913      0.000      -0.304      -0.275
C(countyfips)[T.6087]        -0.2654      0.007    -37.035      0.000      -0.279      -0.251
C(countyfips)[T.6089]        -0.2676      0.011    -23.973      0.000      -0.289      -0.246
C(countyfips)[T.6095]        -0.2248      0.006    -34.606      0.000      -0.238      -0.212
C(countyfips)[T.6099]        -0.2436      0.004    -56.093      0.000      -0.252      -0.235
C(countyfips)[T.6101]        -0.2384      0.009    -26.382      0.000      -0.256      -0.221
C(countyfips)[T.6107]        -0.2126      0.010    -20.551      0.000      -0.233      -0.192
C(countyfips)[T.6111]        -0.1922      0.008    -25.556      0.000      -0.207      -0.177
C(countyfips)[T.6113]        -0.2387      0.006    -37.273      0.000      -0.251      -0.226
C(countyfips)[T.8001]        -0.2162      0.006    -37.535      0.000      -0.227      -0.205
C(countyfips)[T.8005]        -0.2015      0.005    -37.450      0.000      -0.212      -0.191
C(countyfips)[T.8013]        -0.3919      0.007    -57.554      0.000      -0.405      -0.379
C(countyfips)[T.8014]        -0.1585      0.006    -24.718      0.000      -0.171      -0.146
C(countyfips)[T.8031]        -0.3065      0.006    -49.330      0.000      -0.319      -0.294
C(countyfips)[T.8035]        -0.0605      0.006    -10.086      0.000      -0.072      -0.049
C(countyfips)[T.8037]        -0.2328      0.006    -40.591      0.000      -0.244      -0.222
C(countyfips)[T.8041]        -0.2560      0.008    -31.264      0.000      -0.272      -0.240
C(countyfips)[T.8045]        -0.2479      0.005    -47.170      0.000      -0.258      -0.238
C(countyfips)[T.8059]        -0.2318      0.004    -57.283      0.000      -0.240      -0.224
C(countyfips)[T.8077]        -0.2325      0.002   -126.331      0.000      -0.236      -0.229
C(countyfips)[T.8101]        -0.2078      0.004    -52.738      0.000      -0.216      -0.200
C(countyfips)[T.8107]        -0.2276      0.011    -20.045      0.000      -0.250      -0.205
C(countyfips)[T.8117]        -0.2925      0.010    -30.439      0.000      -0.311      -0.274
C(countyfips)[T.8123]        -0.1464      0.005    -28.601      0.000      -0.156      -0.136
C(countyfips)[T.9001]        -0.1489      0.006    -25.063      0.000      -0.160      -0.137
C(countyfips)[T.9003]        -0.1992      0.005    -38.869      0.000      -0.209      -0.189
C(countyfips)[T.9005]        -0.0804      0.008    -10.385      0.000      -0.096      -0.065
C(countyfips)[T.9007]        -0.1446      0.007    -20.378      0.000      -0.158      -0.131
C(countyfips)[T.9009]        -0.2079      0.006    -35.606      0.000      -0.219      -0.196
C(countyfips)[T.9011]        -0.1479      0.007    -20.451      0.000      -0.162      -0.134
C(countyfips)[T.9013]        -0.1868      0.008    -24.502      0.000      -0.202      -0.172
C(countyfips)[T.10001]       -0.1669      0.011    -15.093      0.000      -0.189      -0.145
C(countyfips)[T.10003]       -0.1944      0.011    -18.171      0.000      -0.215      -0.173
C(countyfips)[T.12001]       -0.2293      0.007    -31.744      0.000      -0.243      -0.215
C(countyfips)[T.12009]       -0.0768      0.007    -11.220      0.000      -0.090      -0.063
C(countyfips)[T.12011]       -0.1840      0.005    -34.959      0.000      -0.194      -0.174
C(countyfips)[T.12015]        0.1833      0.004     41.412      0.000       0.175       0.192
C(countyfips)[T.12017]        0.0483      0.004     12.541      0.000       0.041       0.056
C(countyfips)[T.12019]        0.0224      0.005      4.317      0.000       0.012       0.033
C(countyfips)[T.12021]        0.1341      0.005     26.513      0.000       0.124       0.144
C(countyfips)[T.12023]       -0.1447      0.003    -46.889      0.000      -0.151      -0.139
C(countyfips)[T.12031]       -0.1628      0.005    -35.209      0.000      -0.172      -0.154
C(countyfips)[T.12033]       -0.1683      0.005    -31.849      0.000      -0.179      -0.158
C(countyfips)[T.12035]        0.1135      0.005     24.588      0.000       0.104       0.123
C(countyfips)[T.12053]        0.0090      0.004      2.035      0.042       0.000       0.018
C(countyfips)[T.12055]       -0.0612      0.011     -5.811      0.000      -0.082      -0.041
C(countyfips)[T.12057]       -0.1689      0.005    -32.972      0.000      -0.179      -0.159
C(countyfips)[T.12061]        0.0123      0.004      3.038      0.002       0.004       0.020
C(countyfips)[T.12069]        0.0194      0.005      3.754      0.000       0.009       0.030
C(countyfips)[T.12071]        0.1512      0.005     31.144      0.000       0.142       0.161
C(countyfips)[T.12073]       -0.2128      0.008    -27.184      0.000      -0.228      -0.197
C(countyfips)[T.12081]        0.0710      0.006     11.375      0.000       0.059       0.083
C(countyfips)[T.12083]       -0.0243      0.005     -4.857      0.000      -0.034      -0.014
C(countyfips)[T.12085]       -0.0165      0.005     -3.376      0.001      -0.026      -0.007
C(countyfips)[T.12086]       -0.2348      0.007    -35.089      0.000      -0.248      -0.222
C(countyfips)[T.12087]       -0.0270      0.007     -3.941      0.000      -0.040      -0.014
C(countyfips)[T.12091]        0.0003      0.008      0.039      0.969      -0.016       0.017
C(countyfips)[T.12095]       -0.2412      0.006    -37.348      0.000      -0.254      -0.229
C(countyfips)[T.12097]       -0.0325      0.006     -5.589      0.000      -0.044      -0.021
C(countyfips)[T.12099]       -0.1087      0.006    -19.703      0.000      -0.119      -0.098
C(countyfips)[T.12101]        0.0048      0.005      0.895      0.371      -0.006       0.015
C(countyfips)[T.12103]       -0.1230      0.006    -21.784      0.000      -0.134      -0.112
C(countyfips)[T.12105]       -0.0086      0.004     -2.392      0.017      -0.016      -0.002
C(countyfips)[T.12107]       -0.1368      0.007    -20.761      0.000      -0.150      -0.124
C(countyfips)[T.12109]        0.1041      0.006     16.447      0.000       0.092       0.116
C(countyfips)[T.12111]        0.0148      0.006      2.468      0.014       0.003       0.027
C(countyfips)[T.12113]       -0.0396      0.002    -21.572      0.000      -0.043      -0.036
C(countyfips)[T.12115]        0.1607      0.006     26.177      0.000       0.149       0.173
C(countyfips)[T.12117]       -0.2201      0.007    -32.120      0.000      -0.234      -0.207
C(countyfips)[T.12119]        0.3413      0.005     69.372      0.000       0.332       0.351
C(countyfips)[T.12127]       -0.0382      0.005     -6.958      0.000      -0.049      -0.027
C(countyfips)[T.12131]        0.0873      0.009      9.704      0.000       0.070       0.105
C(countyfips)[T.13013]       -0.1460      0.014    -10.682      0.000      -0.173      -0.119
C(countyfips)[T.13015]       -0.1900      0.009    -20.542      0.000      -0.208      -0.172
C(countyfips)[T.13021]       -0.1660      0.005    -32.653      0.000      -0.176      -0.156
C(countyfips)[T.13031]       -0.1857      0.003    -73.267      0.000      -0.191      -0.181
C(countyfips)[T.13039]       -0.3048      0.006    -52.826      0.000      -0.316      -0.294
C(countyfips)[T.13045]       -0.2111      0.008    -26.973      0.000      -0.226      -0.196
C(countyfips)[T.13051]       -0.2164      0.004    -58.958      0.000      -0.224      -0.209
C(countyfips)[T.13057]       -0.0524      0.004    -12.662      0.000      -0.061      -0.044
C(countyfips)[T.13059]       -0.2931      0.008    -35.864      0.000      -0.309      -0.277
C(countyfips)[T.13063]       -0.2253      0.009    -24.790      0.000      -0.243      -0.207
C(countyfips)[T.13067]       -0.1860      0.006    -32.787      0.000      -0.197      -0.175
C(countyfips)[T.13073]       -0.1191      0.006    -18.413      0.000      -0.132      -0.106
C(countyfips)[T.13077]       -0.0802      0.006    -12.672      0.000      -0.093      -0.068
C(countyfips)[T.13089]       -0.2229      0.006    -39.022      0.000      -0.234      -0.212
C(countyfips)[T.13095]       -0.2152      0.003    -65.329      0.000      -0.222      -0.209
C(countyfips)[T.13097]       -0.2167      0.007    -30.993      0.000      -0.230      -0.203
C(countyfips)[T.13113]       -0.0582      0.006    -10.363      0.000      -0.069      -0.047
C(countyfips)[T.13117]       -0.0397      0.012     -3.314      0.001      -0.063      -0.016
C(countyfips)[T.13121]       -0.2092      0.007    -31.057      0.000      -0.222      -0.196
C(countyfips)[T.13129]       -0.1660      0.012    -14.120      0.000      -0.189      -0.143
C(countyfips)[T.13135]       -0.1637      0.004    -38.524      0.000      -0.172      -0.155
C(countyfips)[T.13139]       -0.1006      0.005    -18.897      0.000      -0.111      -0.090
C(countyfips)[T.13151]       -0.0959      0.004    -21.517      0.000      -0.105      -0.087
C(countyfips)[T.13153]       -0.0992      0.003    -36.064      0.000      -0.105      -0.094
C(countyfips)[T.13179]       -0.3141      0.013    -24.981      0.000      -0.339      -0.289
C(countyfips)[T.13185]       -0.2129      0.009    -24.762      0.000      -0.230      -0.196
C(countyfips)[T.13215]       -0.2907      0.006    -47.190      0.000      -0.303      -0.279
C(countyfips)[T.13217]       -0.0801      0.004    -19.440      0.000      -0.088      -0.072
C(countyfips)[T.13245]       -0.2326      0.006    -39.346      0.000      -0.244      -0.221
C(countyfips)[T.13247]       -0.1606      0.010    -15.926      0.000      -0.180      -0.141
C(countyfips)[T.13275]       -0.1922      0.005    -37.286      0.000      -0.202      -0.182
C(countyfips)[T.13297]       -0.0190      0.003     -5.773      0.000      -0.025      -0.013
C(countyfips)[T.13313]       -0.2197      0.008    -28.377      0.000      -0.235      -0.205
C(countyfips)[T.15003]       -0.3040      0.011    -28.726      0.000      -0.325      -0.283
C(countyfips)[T.16001]       -0.1688      0.006    -28.900      0.000      -0.180      -0.157
C(countyfips)[T.16005]       -0.3246      0.007    -47.067      0.000      -0.338      -0.311
C(countyfips)[T.16017]       -0.1045      0.010    -10.106      0.000      -0.125      -0.084
C(countyfips)[T.16019]       -0.1526      0.008    -19.949      0.000      -0.168      -0.138
C(countyfips)[T.16027]       -0.0915      0.005    -17.070      0.000      -0.102      -0.081
C(countyfips)[T.16055]       -0.0812      0.010     -8.021      0.000      -0.101      -0.061
C(countyfips)[T.17031]       -0.2811      0.006    -45.463      0.000      -0.293      -0.269
C(countyfips)[T.17037]       -0.3074      0.011    -27.886      0.000      -0.329      -0.286
C(countyfips)[T.17043]       -0.2212      0.009    -25.268      0.000      -0.238      -0.204
C(countyfips)[T.17089]       -0.1973      0.006    -34.228      0.000      -0.209      -0.186
C(countyfips)[T.17097]       -0.2212      0.005    -42.994      0.000      -0.231      -0.211
C(countyfips)[T.17099]       -0.2935      0.010    -29.102      0.000      -0.313      -0.274
C(countyfips)[T.17111]       -0.1941      0.012    -15.593      0.000      -0.219      -0.170
C(countyfips)[T.17119]       -0.2587      0.010    -25.318      0.000      -0.279      -0.239
C(countyfips)[T.17143]       -0.3277      0.004    -84.365      0.000      -0.335      -0.320
C(countyfips)[T.17163]       -0.2403      0.012    -19.673      0.000      -0.264      -0.216
C(countyfips)[T.17167]       -0.2491      0.007    -34.882      0.000      -0.263      -0.235
C(countyfips)[T.17183]       -0.3182      0.014    -23.137      0.000      -0.345      -0.291
C(countyfips)[T.17197]       -0.1938      0.007    -29.691      0.000      -0.207      -0.181
C(countyfips)[T.17201]       -0.2768      0.006    -43.637      0.000      -0.289      -0.264
C(countyfips)[T.18003]       -0.2991      0.005    -58.626      0.000      -0.309      -0.289
C(countyfips)[T.18011]       -0.1421      0.007    -19.553      0.000      -0.156      -0.128
C(countyfips)[T.18057]       -0.1214      0.008    -15.964      0.000      -0.136      -0.106
C(countyfips)[T.18063]       -0.1496      0.007    -21.207      0.000      -0.163      -0.136
C(countyfips)[T.18081]       -0.2196      0.010    -22.210      0.000      -0.239      -0.200
C(countyfips)[T.18091]       -0.2893      0.004    -66.184      0.000      -0.298      -0.281
C(countyfips)[T.18097]       -0.3255      0.005    -71.570      0.000      -0.334      -0.317
C(countyfips)[T.18127]       -0.2716      0.009    -31.348      0.000      -0.289      -0.255
C(countyfips)[T.18163]       -0.2107      0.005    -39.496      0.000      -0.221      -0.200
C(countyfips)[T.19013]       -0.3492      0.007    -51.876      0.000      -0.362      -0.336
C(countyfips)[T.19061]       -0.2780      0.004    -62.559      0.000      -0.287      -0.269
C(countyfips)[T.19113]       -0.3575      0.012    -31.077      0.000      -0.380      -0.335
C(countyfips)[T.19153]       -0.2986      0.007    -43.428      0.000      -0.312      -0.285
C(countyfips)[T.19155]       -0.3519      0.005    -65.183      0.000      -0.362      -0.341
C(countyfips)[T.19163]       -0.3204      0.011    -29.201      0.000      -0.342      -0.299
C(countyfips)[T.19169]       -0.3469      0.011    -31.922      0.000      -0.368      -0.326
C(countyfips)[T.19193]       -0.3115      0.009    -36.006      0.000      -0.328      -0.295
C(countyfips)[T.20045]       -0.2793      0.007    -39.316      0.000      -0.293      -0.265
C(countyfips)[T.20173]       -0.4099      0.008    -51.269      0.000      -0.426      -0.394
C(countyfips)[T.20209]       -0.2968      0.009    -31.442      0.000      -0.315      -0.278
C(countyfips)[T.21015]       -0.1647      0.011    -15.207      0.000      -0.186      -0.143
C(countyfips)[T.21037]       -0.2249      0.010    -22.827      0.000      -0.244      -0.206
C(countyfips)[T.21059]       -0.2159      0.005    -44.006      0.000      -0.226      -0.206
C(countyfips)[T.21067]       -0.2530      0.006    -39.833      0.000      -0.265      -0.241
C(countyfips)[T.21111]       -0.2636      0.005    -48.805      0.000      -0.274      -0.253
C(countyfips)[T.21199]       -0.1182      0.009    -13.206      0.000      -0.136      -0.101
C(countyfips)[T.21227]       -0.1774      0.006    -28.195      0.000      -0.190      -0.165
C(countyfips)[T.22005]       -0.1814      0.016    -11.359      0.000      -0.213      -0.150
C(countyfips)[T.22017]       -0.2239      0.005    -41.759      0.000      -0.234      -0.213
C(countyfips)[T.22033]       -0.2318      0.007    -35.451      0.000      -0.245      -0.219
C(countyfips)[T.22051]       -0.2557      0.006    -44.705      0.000      -0.267      -0.245
C(countyfips)[T.22055]       -0.1550      0.006    -26.662      0.000      -0.166      -0.144
C(countyfips)[T.22063]       -0.1370      0.006    -22.099      0.000      -0.149      -0.125
C(countyfips)[T.22071]       -0.2642      0.009    -30.323      0.000      -0.281      -0.247
C(countyfips)[T.22073]       -0.2300      0.003    -76.274      0.000      -0.236      -0.224
C(countyfips)[T.22103]       -0.1013      0.005    -18.489      0.000      -0.112      -0.091
C(countyfips)[T.22105]       -0.1182      0.007    -16.359      0.000      -0.132      -0.104
C(countyfips)[T.22109]       -0.2768      0.004    -67.039      0.000      -0.285      -0.269
C(countyfips)[T.23001]       -0.2289      0.004    -52.745      0.000      -0.237      -0.220
C(countyfips)[T.23005]       -0.1744      0.006    -28.113      0.000      -0.187      -0.162
C(countyfips)[T.23019]       -0.2505      0.014    -18.018      0.000      -0.278      -0.223
C(countyfips)[T.24001]       -0.1970      0.010    -19.655      0.000      -0.217      -0.177
C(countyfips)[T.24003]       -0.1850      0.005    -39.971      0.000      -0.194      -0.176
C(countyfips)[T.24005]       -0.1868      0.006    -33.163      0.000      -0.198      -0.176
C(countyfips)[T.24009]       -0.1187      0.008    -15.761      0.000      -0.133      -0.104
C(countyfips)[T.24013]       -0.1195      0.005    -25.867      0.000      -0.129      -0.110
C(countyfips)[T.24017]       -0.1244      0.009    -14.028      0.000      -0.142      -0.107
C(countyfips)[T.24021]       -0.0593      0.005    -12.192      0.000      -0.069      -0.050
C(countyfips)[T.24025]       -0.1416      0.004    -35.271      0.000      -0.149      -0.134
C(countyfips)[T.24027]       -0.1601      0.009    -18.238      0.000      -0.177      -0.143
C(countyfips)[T.24031]       -0.2312      0.008    -29.545      0.000      -0.247      -0.216
C(countyfips)[T.24033]       -0.2578      0.011    -23.719      0.000      -0.279      -0.237
C(countyfips)[T.24043]       -0.1980      0.005    -38.400      0.000      -0.208      -0.188
C(countyfips)[T.24510]       -0.3040      0.009    -35.203      0.000      -0.321      -0.287
C(countyfips)[T.25001]       -0.0773      0.005    -15.607      0.000      -0.087      -0.068
C(countyfips)[T.25003]       -0.0872      0.012     -7.453      0.000      -0.110      -0.064
C(countyfips)[T.25017]       -0.2633      0.007    -39.160      0.000      -0.276      -0.250
C(countyfips)[T.25021]       -0.2037      0.007    -28.583      0.000      -0.218      -0.190
C(countyfips)[T.25023]       -0.1469      0.006    -24.117      0.000      -0.159      -0.135
C(countyfips)[T.25025]       -0.4819      0.010    -48.353      0.000      -0.501      -0.462
C(countyfips)[T.25027]       -0.2002      0.007    -30.672      0.000      -0.213      -0.187
C(countyfips)[T.26045]       -0.2632      0.005    -50.550      0.000      -0.273      -0.253
C(countyfips)[T.26049]       -0.2560      0.006    -43.612      0.000      -0.267      -0.244
C(countyfips)[T.26065]       -0.3180      0.012    -26.675      0.000      -0.341      -0.295
C(countyfips)[T.26077]       -0.3246      0.011    -28.751      0.000      -0.347      -0.302
C(countyfips)[T.26081]       -0.3015      0.008    -39.101      0.000      -0.317      -0.286
C(countyfips)[T.26099]       -0.2275      0.006    -36.113      0.000      -0.240      -0.215
C(countyfips)[T.26121]       -0.2533      0.010    -24.927      0.000      -0.273      -0.233
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C(countyfips)[T.26139]       -0.2312      0.006    -39.502      0.000      -0.243      -0.220
C(countyfips)[T.26145]       -0.2486      0.005    -53.406      0.000      -0.258      -0.240
C(countyfips)[T.26147]       -0.2374      0.007    -35.977      0.000      -0.250      -0.224
C(countyfips)[T.26161]       -0.3282      0.006    -51.242      0.000      -0.341      -0.316
C(countyfips)[T.26163]       -0.2284      0.009    -26.517      0.000      -0.245      -0.212
C(countyfips)[T.27003]       -0.2595      0.005    -55.973      0.000      -0.269      -0.250
C(countyfips)[T.27005]       -0.2833      0.016    -17.807      0.000      -0.314      -0.252
C(countyfips)[T.27013]       -0.6046      0.007    -85.270      0.000      -0.619      -0.591
C(countyfips)[T.27019]       -0.1470      0.008    -17.429      0.000      -0.163      -0.130
C(countyfips)[T.27025]       -0.1623      0.009    -18.937      0.000      -0.179      -0.145
C(countyfips)[T.27035]       -0.1703      0.017    -10.323      0.000      -0.203      -0.138
C(countyfips)[T.27037]       -0.2500      0.008    -30.291      0.000      -0.266      -0.234
C(countyfips)[T.27053]       -0.3448      0.005    -63.816      0.000      -0.355      -0.334
C(countyfips)[T.27109]       -0.2118      0.005    -46.187      0.000      -0.221      -0.203
C(countyfips)[T.27123]       -0.3410      0.005    -64.595      0.000      -0.351      -0.331
C(countyfips)[T.27131]       -0.1766      0.003    -62.236      0.000      -0.182      -0.171
C(countyfips)[T.27137]       -0.2780      0.002   -153.865      0.000      -0.282      -0.274
C(countyfips)[T.27139]       -0.1979      0.014    -14.598      0.000      -0.225      -0.171
C(countyfips)[T.27145]       -0.2466      0.008    -29.285      0.000      -0.263      -0.230
C(countyfips)[T.27163]       -0.1792      0.008    -21.646      0.000      -0.195      -0.163
C(countyfips)[T.27171]       -0.1570      0.006    -26.022      0.000      -0.169      -0.145
C(countyfips)[T.28033]       -0.1017      0.005    -20.100      0.000      -0.112      -0.092
C(countyfips)[T.28047]       -0.2135      0.007    -32.395      0.000      -0.226      -0.201
C(countyfips)[T.28049]       -0.2833      0.004    -68.127      0.000      -0.291      -0.275
C(countyfips)[T.28059]       -0.1192      0.016     -7.517      0.000      -0.150      -0.088
C(countyfips)[T.28089]       -0.1023      0.002    -47.896      0.000      -0.106      -0.098
C(countyfips)[T.28121]       -0.1244      0.008    -16.430      0.000      -0.139      -0.110
C(countyfips)[T.29019]       -0.2440      0.010    -24.954      0.000      -0.263      -0.225
C(countyfips)[T.29021]       -0.2948      0.007    -44.118      0.000      -0.308      -0.282
C(countyfips)[T.29029]       -0.1856      0.009    -20.421      0.000      -0.203      -0.168
C(countyfips)[T.29031]       -0.2531      0.005    -47.238      0.000      -0.264      -0.243
C(countyfips)[T.29047]       -0.1987      0.007    -26.627      0.000      -0.213      -0.184
C(countyfips)[T.29071]       -0.1679      0.004    -43.591      0.000      -0.175      -0.160
C(countyfips)[T.29077]       -0.3715      0.007    -56.125      0.000      -0.384      -0.359
C(countyfips)[T.29095]       -0.2560      0.005    -49.053      0.000      -0.266      -0.246
C(countyfips)[T.29097]       -0.2696      0.002   -137.943      0.000      -0.273      -0.266
C(countyfips)[T.29099]       -0.1570      0.012    -13.472      0.000      -0.180      -0.134
C(countyfips)[T.29145]       -0.2053      0.012    -17.326      0.000      -0.229      -0.182
C(countyfips)[T.29183]       -0.1134      0.005    -24.118      0.000      -0.123      -0.104
C(countyfips)[T.29189]       -0.1961      0.005    -36.516      0.000      -0.207      -0.186
C(countyfips)[T.29510]       -0.3557      0.007    -47.651      0.000      -0.370      -0.341
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C(countyfips)[T.30049]       -0.1692      0.009    -19.505      0.000      -0.186      -0.152
C(countyfips)[T.30063]       -0.2446      0.003    -81.004      0.000      -0.251      -0.239
C(countyfips)[T.30111]       -0.2856      0.005    -56.597      0.000      -0.295      -0.276
C(countyfips)[T.31019]       -0.3359      0.006    -55.644      0.000      -0.348      -0.324
C(countyfips)[T.31055]       -0.2835      0.004    -70.762      0.000      -0.291      -0.276
C(countyfips)[T.31079]       -0.3900      0.002   -238.747      0.000      -0.393      -0.387
C(countyfips)[T.31109]       -0.3656      0.004    -91.951      0.000      -0.373      -0.358
C(countyfips)[T.31153]       -0.1854      0.010    -18.464      0.000      -0.205      -0.166
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C(countyfips)[T.32510]       -0.2789      0.004    -68.055      0.000      -0.287      -0.271
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C(countyfips)[T.33011]       -0.1957      0.007    -26.972      0.000      -0.210      -0.181
C(countyfips)[T.33015]       -0.1425      0.006    -22.224      0.000      -0.155      -0.130
C(countyfips)[T.33017]       -0.1942      0.006    -32.470      0.000      -0.206      -0.182
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C(countyfips)[T.34009]       -0.1175      0.018     -6.473      0.000      -0.153      -0.082
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C(countyfips)[T.41035]       -0.1371      0.011    -12.228      0.000      -0.159      -0.115
C(countyfips)[T.41039]       -0.2578      0.006    -46.160      0.000      -0.269      -0.247
C(countyfips)[T.41041]       -0.2566      0.013    -19.677      0.000      -0.282      -0.231
C(countyfips)[T.41043]       -0.1596      0.007    -21.634      0.000      -0.174      -0.145
C(countyfips)[T.41047]       -0.4008      0.006    -61.745      0.000      -0.414      -0.388
C(countyfips)[T.41051]       -0.3398      0.007    -48.268      0.000      -0.354      -0.326
C(countyfips)[T.41059]       -0.3268      0.012    -28.317      0.000      -0.349      -0.304
C(countyfips)[T.41067]       -0.1957      0.005    -36.891      0.000      -0.206      -0.185
C(countyfips)[T.42003]       -0.2726      0.005    -50.136      0.000      -0.283      -0.262
C(countyfips)[T.42007]       -0.2240      0.007    -33.540      0.000      -0.237      -0.211
C(countyfips)[T.42011]       -0.2146      0.006    -33.790      0.000      -0.227      -0.202
C(countyfips)[T.42013]       -0.1908      0.007    -26.262      0.000      -0.205      -0.177
C(countyfips)[T.42015]       -0.2379      0.004    -53.175      0.000      -0.247      -0.229
C(countyfips)[T.42017]       -0.1662      0.007    -22.542      0.000      -0.181      -0.152
C(countyfips)[T.42019]       -0.1770      0.007    -26.439      0.000      -0.190      -0.164
C(countyfips)[T.42021]       -0.2121      0.007    -28.377      0.000      -0.227      -0.197
C(countyfips)[T.42027]       -0.2515      0.008    -32.397      0.000      -0.267      -0.236
C(countyfips)[T.42029]       -0.1518      0.006    -24.248      0.000      -0.164      -0.140
C(countyfips)[T.42033]       -0.2384      0.006    -37.734      0.000      -0.251      -0.226
C(countyfips)[T.42041]       -0.1633      0.006    -28.851      0.000      -0.174      -0.152
C(countyfips)[T.42043]       -0.2370      0.006    -37.360      0.000      -0.249      -0.225
C(countyfips)[T.42045]       -0.2116      0.006    -35.662      0.000      -0.223      -0.200
C(countyfips)[T.42049]       -0.2555      0.007    -37.850      0.000      -0.269      -0.242
C(countyfips)[T.42051]       -0.2118      0.012    -17.414      0.000      -0.236      -0.188
C(countyfips)[T.42055]       -0.1753      0.009    -19.912      0.000      -0.193      -0.158
C(countyfips)[T.42063]       -0.1943      0.009    -21.417      0.000      -0.212      -0.176
C(countyfips)[T.42065]       -0.2156      0.007    -31.783      0.000      -0.229      -0.202
C(countyfips)[T.42069]       -0.2184      0.005    -42.846      0.000      -0.228      -0.208
C(countyfips)[T.42071]       -0.2237      0.006    -34.943      0.000      -0.236      -0.211
C(countyfips)[T.42073]       -0.2097      0.004    -48.880      0.000      -0.218      -0.201
C(countyfips)[T.42075]       -0.1906      0.008    -25.263      0.000      -0.205      -0.176
C(countyfips)[T.42077]       -0.1972      0.005    -40.243      0.000      -0.207      -0.188
C(countyfips)[T.42079]       -0.1687      0.008    -21.030      0.000      -0.184      -0.153
C(countyfips)[T.42085]       -0.3024      0.014    -22.105      0.000      -0.329      -0.276
C(countyfips)[T.42089]       -0.2324      0.008    -29.295      0.000      -0.248      -0.217
C(countyfips)[T.42091]       -0.1463      0.005    -27.984      0.000      -0.157      -0.136
C(countyfips)[T.42095]       -0.1896      0.007    -28.327      0.000      -0.203      -0.176
C(countyfips)[T.42097]       -0.2010      0.006    -32.812      0.000      -0.213      -0.189
C(countyfips)[T.42103]       -0.1387      0.008    -16.733      0.000      -0.155      -0.122
C(countyfips)[T.42115]       -0.2701      0.011    -24.373      0.000      -0.292      -0.248
C(countyfips)[T.42125]       -0.1667      0.006    -30.050      0.000      -0.178      -0.156
C(countyfips)[T.42129]       -0.2145      0.010    -20.531      0.000      -0.235      -0.194
C(countyfips)[T.42133]       -0.2009      0.007    -28.988      0.000      -0.214      -0.187
C(countyfips)[T.44003]       -0.1238      0.009    -13.997      0.000      -0.141      -0.106
C(countyfips)[T.44007]       -0.2282      0.006    -37.200      0.000      -0.240      -0.216
C(countyfips)[T.44009]       -0.1065      0.003    -33.823      0.000      -0.113      -0.100
C(countyfips)[T.45003]       -0.1075      0.006    -16.854      0.000      -0.120      -0.095
C(countyfips)[T.45007]       -0.1364      0.009    -15.362      0.000      -0.154      -0.119
C(countyfips)[T.45015]       -0.0839      0.003    -28.604      0.000      -0.090      -0.078
C(countyfips)[T.45019]       -0.1682      0.003    -48.338      0.000      -0.175      -0.161
C(countyfips)[T.45035]       -0.1266      0.006    -19.520      0.000      -0.139      -0.114
C(countyfips)[T.45043]       -0.0403      0.010     -4.238      0.000      -0.059      -0.022
C(countyfips)[T.45045]       -0.1220      0.006    -20.974      0.000      -0.133      -0.111
C(countyfips)[T.45051]        0.0256      0.008      3.368      0.001       0.011       0.041
C(countyfips)[T.45057]        0.0707      0.006     11.780      0.000       0.059       0.082
C(countyfips)[T.45063]       -0.1269      0.007    -17.519      0.000      -0.141      -0.113
C(countyfips)[T.45077]       -0.1680      0.012    -14.414      0.000      -0.191      -0.145
C(countyfips)[T.45079]       -0.2066      0.007    -29.351      0.000      -0.220      -0.193
C(countyfips)[T.45083]       -0.1425      0.005    -30.591      0.000      -0.152      -0.133
C(countyfips)[T.45085]       -0.1999      0.004    -47.364      0.000      -0.208      -0.192
C(countyfips)[T.45091]       -0.1023      0.004    -26.149      0.000      -0.110      -0.095
C(countyfips)[T.46099]       -0.2961      0.003   -109.683      0.000      -0.301      -0.291
C(countyfips)[T.46103]       -0.1467      0.012    -12.009      0.000      -0.171      -0.123
C(countyfips)[T.47001]       -0.1141      0.004    -29.203      0.000      -0.122      -0.106
C(countyfips)[T.47009]       -0.1046      0.009    -11.948      0.000      -0.122      -0.087
C(countyfips)[T.47011]       -0.1531      0.008    -19.474      0.000      -0.168      -0.138
C(countyfips)[T.47037]       -0.3092      0.005    -58.972      0.000      -0.319      -0.299
C(countyfips)[T.47043]       -0.0984      0.006    -15.649      0.000      -0.111      -0.086
C(countyfips)[T.47065]       -0.1855      0.009    -21.396      0.000      -0.202      -0.169
C(countyfips)[T.47093]       -0.1571      0.006    -26.610      0.000      -0.169      -0.146
C(countyfips)[T.47113]       -0.1464      0.009    -16.660      0.000      -0.164      -0.129
C(countyfips)[T.47141]       -0.1081      0.009    -12.260      0.000      -0.125      -0.091
C(countyfips)[T.47149]       -0.1456      0.002    -60.149      0.000      -0.150      -0.141
C(countyfips)[T.47155]       -0.2071      0.014    -14.534      0.000      -0.235      -0.179
C(countyfips)[T.47157]       -0.2078      0.006    -33.712      0.000      -0.220      -0.196
C(countyfips)[T.47163]       -0.1094      0.003    -39.289      0.000      -0.115      -0.104
C(countyfips)[T.47165]       -0.1125      0.002    -45.648      0.000      -0.117      -0.108
C(countyfips)[T.47179]       -0.1582      0.006    -25.959      0.000      -0.170      -0.146
C(countyfips)[T.47187]       -0.0490      0.004    -11.526      0.000      -0.057      -0.041
C(countyfips)[T.47189]       -0.0158      0.003     -5.618      0.000      -0.021      -0.010
C(countyfips)[T.48013]       -0.0743      0.007    -10.940      0.000      -0.088      -0.061
C(countyfips)[T.48021]       -0.0130      0.005     -2.786      0.005      -0.022      -0.004
C(countyfips)[T.48027]       -0.2447      0.010    -23.721      0.000      -0.265      -0.224
C(countyfips)[T.48029]       -0.1971      0.007    -29.139      0.000      -0.210      -0.184
C(countyfips)[T.48039]       -0.1686      0.009    -19.290      0.000      -0.186      -0.151
C(countyfips)[T.48041]       -0.2779      0.005    -58.916      0.000      -0.287      -0.269
C(countyfips)[T.48061]       -0.0649      0.006    -10.606      0.000      -0.077      -0.053
C(countyfips)[T.48085]       -0.0561      0.009     -6.116      0.000      -0.074      -0.038
C(countyfips)[T.48091]        0.1217      0.002     51.493      0.000       0.117       0.126
C(countyfips)[T.48113]       -0.2482      0.006    -43.195      0.000      -0.260      -0.237
C(countyfips)[T.48121]       -0.0846      0.006    -15.245      0.000      -0.096      -0.074
C(countyfips)[T.48139]       -0.0134      0.005     -2.763      0.006      -0.023      -0.004
C(countyfips)[T.48141]       -0.1978      0.005    -42.536      0.000      -0.207      -0.189
C(countyfips)[T.48157]       -0.0721      0.008     -8.556      0.000      -0.089      -0.056
C(countyfips)[T.48167]       -0.1896      0.006    -29.577      0.000      -0.202      -0.177
C(countyfips)[T.48171]       -0.0852      0.008    -10.409      0.000      -0.101      -0.069
C(countyfips)[T.48181]       -0.0831      0.006    -13.791      0.000      -0.095      -0.071
C(countyfips)[T.48183]       -0.2074      0.007    -29.803      0.000      -0.221      -0.194
C(countyfips)[T.48187]       -0.0965      0.004    -23.900      0.000      -0.104      -0.089
C(countyfips)[T.48201]       -0.2027      0.006    -36.569      0.000      -0.214      -0.192
C(countyfips)[T.48209]       -0.0590      0.008     -7.121      0.000      -0.075      -0.043
C(countyfips)[T.48215]       -0.1034      0.006    -16.589      0.000      -0.116      -0.091
C(countyfips)[T.48221]       -0.0184      0.009     -2.120      0.034      -0.035      -0.001
C(countyfips)[T.48231]       -0.1060      0.009    -12.388      0.000      -0.123      -0.089
C(countyfips)[T.48245]       -0.2625      0.008    -33.832      0.000      -0.278      -0.247
C(countyfips)[T.48251]       -0.0355      0.004     -9.662      0.000      -0.043      -0.028
C(countyfips)[T.48257]        0.1743      0.007     24.976      0.000       0.161       0.188
C(countyfips)[T.48265]       -0.1827      0.014    -12.769      0.000      -0.211      -0.155
C(countyfips)[T.48291]       -0.0312      0.007     -4.269      0.000      -0.045      -0.017
C(countyfips)[T.48303]       -0.2330      0.003    -77.233      0.000      -0.239      -0.227
C(countyfips)[T.48309]       -0.1690      0.004    -42.227      0.000      -0.177      -0.161
C(countyfips)[T.48329]       -0.3940      0.008    -47.501      0.000      -0.410      -0.378
C(countyfips)[T.48339]       -0.0331      0.005     -6.673      0.000      -0.043      -0.023
C(countyfips)[T.48355]       -0.1946      0.005    -40.232      0.000      -0.204      -0.185
C(countyfips)[T.48367]        0.0260      0.011      2.313      0.021       0.004       0.048
C(countyfips)[T.48375]       -0.2348      0.006    -38.814      0.000      -0.247      -0.223
C(countyfips)[T.48381]       -0.2153      0.006    -37.119      0.000      -0.227      -0.204
C(countyfips)[T.48397]        0.1113      0.003     36.002      0.000       0.105       0.117
C(countyfips)[T.48423]       -0.1279      0.007    -19.547      0.000      -0.141      -0.115
C(countyfips)[T.48439]       -0.2042      0.006    -32.409      0.000      -0.217      -0.192
C(countyfips)[T.48451]       -0.2655      0.003    -86.679      0.000      -0.272      -0.260
C(countyfips)[T.48453]       -0.2353      0.007    -33.127      0.000      -0.249      -0.221
C(countyfips)[T.48469]       -0.2237      0.010    -22.068      0.000      -0.244      -0.204
C(countyfips)[T.48471]       -0.1727      0.004    -47.452      0.000      -0.180      -0.166
C(countyfips)[T.48479]       -0.1890      0.009    -21.211      0.000      -0.206      -0.172
C(countyfips)[T.48485]       -0.8925      0.004   -215.564      0.000      -0.901      -0.884
C(countyfips)[T.48491]        0.0145      0.007      2.078      0.038       0.001       0.028
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C(countyfips)[T.49035]       -0.2801      0.006    -49.923      0.000      -0.291      -0.269
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C(countyfips)[T.49045]       -0.1052      0.014     -7.685      0.000      -0.132      -0.078
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C(countyfips)[T.49057]       -0.2046      0.006    -33.807      0.000      -0.216      -0.193
C(countyfips)[T.50021]       -0.1765      0.008    -21.506      0.000      -0.193      -0.160
C(countyfips)[T.50025]       -0.1237      0.006    -21.287      0.000      -0.135      -0.112
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C(countyfips)[T.51013]       -0.4636      0.012    -39.292      0.000      -0.487      -0.441
C(countyfips)[T.51015]       -0.2183      0.006    -36.330      0.000      -0.230      -0.206
C(countyfips)[T.51019]       -0.1436      0.008    -19.111      0.000      -0.158      -0.129
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C(countyfips)[T.51047]       -0.0712      0.012     -5.758      0.000      -0.095      -0.047
C(countyfips)[T.51059]       -0.2357      0.008    -29.804      0.000      -0.251      -0.220
C(countyfips)[T.51061]       -0.1480      0.009    -16.475      0.000      -0.166      -0.130
C(countyfips)[T.51069]       -0.1391      0.011    -12.848      0.000      -0.160      -0.118
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C(countyfips)[T.51087]       -0.1914      0.010    -19.359      0.000      -0.211      -0.172
C(countyfips)[T.51095]       -0.0901      0.007    -13.431      0.000      -0.103      -0.077
C(countyfips)[T.51107]       -0.1105      0.005    -20.916      0.000      -0.121      -0.100
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C(countyfips)[T.51153]       -0.2232      0.008    -28.057      0.000      -0.239      -0.208
C(countyfips)[T.51161]       -0.1368      0.004    -32.081      0.000      -0.145      -0.128
C(countyfips)[T.51177]       -0.0760      0.007    -11.576      0.000      -0.089      -0.063
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C(countyfips)[T.51199]       -0.1423      0.006    -24.411      0.000      -0.154      -0.131
C(countyfips)[T.51510]       -0.3601      0.006    -61.313      0.000      -0.372      -0.349
C(countyfips)[T.51550]       -0.1724      0.007    -25.258      0.000      -0.186      -0.159
C(countyfips)[T.51630]       -0.1913      0.008    -23.802      0.000      -0.207      -0.176
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C(countyfips)[T.51710]       -0.3237      0.004    -74.561      0.000      -0.332      -0.315
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C(countyfips)[T.55025]       -0.2957      0.006    -50.507      0.000      -0.307      -0.284
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C(countyfips)[T.55039]       -0.2438      0.003    -73.457      0.000      -0.250      -0.237
C(countyfips)[T.55059]       -0.2799      0.004    -70.906      0.000      -0.288      -0.272
C(countyfips)[T.55063]       -0.3319      0.006    -56.445      0.000      -0.343      -0.320
C(countyfips)[T.55073]       -0.2270      0.006    -36.657      0.000      -0.239      -0.215
C(countyfips)[T.55079]       -0.3244      0.006    -57.450      0.000      -0.335      -0.313
C(countyfips)[T.55087]       -0.2558      0.006    -42.983      0.000      -0.267      -0.244
C(countyfips)[T.55089]       -0.1371      0.006    -23.018      0.000      -0.149      -0.125
C(countyfips)[T.55095]       -0.2549      0.015    -17.196      0.000      -0.284      -0.226
C(countyfips)[T.55097]       -0.2864      0.005    -58.639      0.000      -0.296      -0.277
C(countyfips)[T.55101]       -0.2398      0.009    -26.823      0.000      -0.257      -0.222
C(countyfips)[T.55111]       -0.2617      0.010    -26.831      0.000      -0.281      -0.243
C(countyfips)[T.55117]       -0.3221      0.008    -41.549      0.000      -0.337      -0.307
C(countyfips)[T.55127]       -0.2751      0.010    -27.558      0.000      -0.295      -0.256
C(countyfips)[T.55131]       -0.2230      0.010    -22.892      0.000      -0.242      -0.204
C(countyfips)[T.55133]       -0.1516      0.004    -34.757      0.000      -0.160      -0.143
C(countyfips)[T.55139]       -0.2760      0.011    -24.190      0.000      -0.298      -0.254
C(countyfips)[T.56021]       -0.2088      0.006    -35.501      0.000      -0.220      -0.197
C(countyfips)[T.56025]       -0.1646      0.005    -35.153      0.000      -0.174      -0.155
C(month)[T.2.0]              -0.0282      0.008     -3.314      0.001      -0.045      -0.012
C(month)[T.3.0]              -0.0258      0.014     -1.866      0.062      -0.053       0.001
C(month)[T.4.0]              -0.0133      0.018     -0.755      0.450      -0.048       0.021
C(month)[T.5.0]              -0.0066      0.023     -0.289      0.772      -0.051       0.038
C(month)[T.6.0]              -0.0122      0.018     -0.673      0.501      -0.048       0.023
C(month)[T.7.0]              -0.0318      0.013     -2.393      0.017      -0.058      -0.006
C(month)[T.8.0]              -0.0315      0.012     -2.736      0.006      -0.054      -0.009
C(month)[T.9.0]              -0.0337      0.009     -3.768      0.000      -0.051      -0.016
C(month)[T.10.0]             -0.0524      0.009     -5.733      0.000      -0.070      -0.034
C(month)[T.11.0]             -0.0350      0.006     -5.757      0.000      -0.047      -0.023
C(month)[T.12.0]             -0.0206      0.005     -4.331      0.000      -0.030      -0.011
spend_all                    -0.0012      0.000     -6.409      0.000      -0.002      -0.001
gps_retail_and_recreation     0.0017      0.000      5.700      0.000       0.001       0.002
emp                          -0.0014      0.000     -3.697      0.000      -0.002      -0.001
revenue_all                  -0.0004      0.000     -2.525      0.012      -0.001   -9.02e-05
==============================================================================
Omnibus:                     6169.899   Durbin-Watson:                   0.600
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          2257769.413
Skew:                          -0.470   Prob(JB):                         0.00
Kurtosis:                      60.605   Cond. No.                     2.48e+04
==============================================================================

Notes:
[1] Standard Errors are robust to cluster correlation (cluster)
[2] The condition number is large, 2.48e+04. This might indicate that there are
strong multicollinearity or other numerical problems.

The economic variables are slightly less significant, as observed by the lower in magnitude t-stats, but they all remian significant at at least the 5% level, showing that the correlations are robust to this type of standard error clustering.

Overall, these results show that when holding fixed county and month, the average correlation between migration and the economic variables is negative for spending, employment, and small business revenue. On the other hand, the correlations are positive for the foot traffic variable. This raises the question of whether these variables are useful for predicting future migration flows, which is explored in the next section.

Predicting future migration¶

With these data relationships in mind, I now move to predicting migration flows.

First, I prepare the data by rescaling the migration flows to have unit variance and a mean of 0. I perform this calculation separately for each county, then reshape the data so that one column of data represents data for one county.

In [39]:
# Step 1: scale data to have unit variance
df_std = df_usps
df_std = df_std[['countyfips', 'year', 'month', 'net_flow_pop', 'time']]

# Z-score the data
zscore = lambda x: (x - x.mean()) / x.std()
df_std['net_flow_pop_std'] = df_std.groupby([df_std['countyfips']])[['net_flow_pop']].apply(zscore)
county_obs = df_std.groupby(['countyfips']).count()
In [40]:
# Checks that the transformation worked
#print(df_std.groupby([df_std['countyfips']])[['net_flow_pop', 'net_flow_pop_std']].mean())
#print(df_std.groupby([df_std['countyfips']])[['net_flow_pop', 'net_flow_pop_std']].std())
In [41]:
# Reshape data
df_std = df_std.pivot(index=['time'], columns=['countyfips'], values=['net_flow_pop', 'net_flow_pop_std'])
In [42]:
df_std.head()
Out[42]:
net_flow_pop ... net_flow_pop_std
countyfips 1001 1003 1005 1007 1009 1011 1013 1015 1017 1019 ... 56027 56029 56031 56033 56035 56037 56039 56041 56043 56045
time
2018-11-01 -0.002463 0.486347 -0.076902 -0.016045 0.028672 0.026248 -0.007818 -0.042382 -0.090433 -0.070250 ... 0.486282 -1.127154 -1.538584 -1.525380 -1.154384 -0.864668 -0.822638 -1.657379 -1.609753 -0.240388
2018-12-01 -0.011114 1.090342 -0.116814 0.045118 -0.036260 -0.012263 -0.052431 -0.016903 -0.084774 -0.082339 ... -0.770732 -0.485071 -1.013551 -1.192526 -0.445806 -0.864668 0.366710 -0.612683 -0.975483 -0.107543
2019-01-01 0.055200 0.718268 -0.085444 -0.019537 0.003207 -0.094868 -0.070153 -0.106824 -0.057209 -0.101451 ... -0.771012 -0.814903 0.167937 0.360794 -0.500537 -1.886175 -0.159432 -0.398387 -1.672146 -1.222200
2019-02-01 -0.122490 -0.077906 0.001718 -0.124315 0.032611 -0.041657 -0.069772 -0.032318 0.007432 0.066207 ... 0.565250 -0.548213 -0.547199 -0.241514 -0.065961 -0.202069 -0.032459 -0.585896 -0.798643 0.406359
2019-03-01 -0.095691 -0.527293 -0.026166 -0.169704 0.001491 -0.066334 -0.169475 -0.046560 -0.055500 -0.033070 ... -0.928029 0.005796 0.540727 -0.621918 -0.047091 -0.340111 -0.635636 0.378439 -0.486677 -0.367735

5 rows × 6260 columns

Now that I have the data rescaled by county, I look at 5 random counties to see their trends over time. I will use these counties as test cases to show how well the decomposition is working.

In [43]:
# Generate rescaled timeseries plots
fig, ax = plt.subplots(3,2, figsize=(16,16))
ax = ax.flatten()
for i, cty in enumerate([1001, 47083, 6083, 40031, 30067]):
    ax[i] = sns.lineplot(data= df_std['net_flow_pop_std'][cty], x='time', y=df_std['net_flow_pop_std'][cty], ax=ax[i])
    ax[i].set_ylabel('Net Flow rel Population (Std.)')
    ax[i].set_xlabel("Year-Month")
    ax[i].set_title("County Code:" + str(cty))
    
plt.show()

These plots show that there is clearly strong seasonal variation for each county, which was also observed earlier. To get rid of the seasonal and any trend components in the data, I perform an STL decomposition using statsmodels.tsa.seasonal.seasonal_decompose. I use additive models for this since the variation appears somewhat consistent over time. One of my functions plots the decomposition for individual counties, while the other I'll use to perform the decomposition on every county.

In [44]:
# Functions come from Stephen Elston's Lesson 11 workbook
def decomp_ts(ts, freq = 'M', model = 'additive'):
    res = sts.seasonal_decompose(ts, period=12, model = model) 
    #res.plot()
    return(pd.DataFrame({'resid': res.resid, 
                         'trend': res.trend, 
                         'seasonal': res.seasonal},
                       index = ts.index) )

def decomp_ts_plot(ts, freq = 'M', model = 'additive'):
    res = sts.seasonal_decompose(ts, period=12, model = model) 
    res.plot()
    return(pd.DataFrame({'resid': res.resid, 
                         'trend': res.trend, 
                         'seasonal': res.seasonal},
                       index = ts.index) )

decomp1 = decomp_ts_plot(df_std['net_flow_pop_std'][1001], model='additive')
decomp2 = decomp_ts_plot(df_std['net_flow_pop_std'][47083], model='additive')
decomp3 = decomp_ts_plot(df_std['net_flow_pop_std'][6083], model='additive')
decomp4 = decomp_ts_plot(df_std['net_flow_pop_std'][40031], model='additive')
decomp5 = decomp_ts_plot(df_std['net_flow_pop_std'][30067], model='additive')
In [45]:
# Only use counties with non-missing values
kept_counties = county_obs[county_obs['year'] == 47]
counties = df_usps.merge(kept_counties.reset_index()['countyfips'], on='countyfips', how='inner')
counties = counties['countyfips'].unique()

#warnings.filterwarnings("ignore")
# Strip seasonal and trend from data
def county_STL(df, var, counties=counties):
    # Create empty df
    resid_df = pd.DataFrame(index=df_std.index)
    seasonal_df = pd.DataFrame(index=df_std.index)
    trend_df = pd.DataFrame(index=df_std.index)

    for county in counties:
        #print(county)
        decomp = decomp_ts(df[var][county], model='additive')
        resid_df[county] = decomp.resid
        seasonal_df[county] = decomp.seasonal
        trend_df[county] = decomp.trend 
    
    return resid_df, seasonal_df, trend_df
In [ ]:
# Generate dataframes with decompositions for all counties
resid_df, seasonal_df, trend_df = county_STL(df_std, 'net_flow_pop_std')

These plots show the STL decomposition for the 5 test counties. The seasonal and trend components are clear and seem to match well with the plotted timeseries. The residuals look close to white noise, and I test this in the following ACF and PACF plots.

In [47]:
# Functions all come from Stephen Elston's Lesson 11 notebook
def dist_ts(ts, lab = '', bins = 40):
    _,ax = plt.subplots(1,2,figsize=(10,4))
    ## Plot the histogram with labels
    ts.hist(ax = ax[0], bins = bins, alpha = 0.5);
    ax[0].set_xlabel('Value');
    ax[0].set_ylabel('Frequency');
    ax[0].set_title('Histogram of ' + lab);
    ## Plot the q-q plot on the other axes
    ss.probplot(ts, plot = ax[1]);
    
def auto_partial_corr_plot(ts):
    _,ax = plt.subplots(2,1, figsize=(8,8))
    _=splt.plot_acf(ts, lags = 16, ax=ax[0]);
    _=splt.plot_pacf(ts, lags = 16, method='yw', ax=ax[1]);
    
def DF_Test(ts):
    stationary = adfuller(ts)
    ## Print the results
    print('D-F statistic = ' + str(stationary[0]))
    print('p-value = ' + str(stationary[1]))
    print('number of lags used = ' + str(stationary[2]))
    print('Critical value at 5% confidence = ' + str(stationary[4]['5%']))
    print('Critical value at 10% confidence = ' + str(stationary[4]['10%']))   
In [48]:
# Function for testing the stationarity of all counties
def DF_Test_full(ts, counties=counties):
    
    df_p_vals = []
    
    # Loop through counties
    for county in counties:
        stationary = adfuller(ts[county][6:-6])
        # P-value test
        if stationary[1] < 0.05:
            test = True
        else:
            test = False
        df_p_vals.append(test)
        
    return df_p_vals

# Run tests
DF_p_vals = DF_Test_full(resid_df)

To get a sense of how well the STL decomposition did with removing the stationary components of the timeseries, I build a function that returns True if the timeseries of the residuals is stationary and False if it is not, using the augmented Dicky Fuller test. This allows me to calculate the percent of counties with stationary timeseries, according to the test:

In [49]:
print("Percent of stationary counties: {}%".format(np.round(DF_p_vals.count(True) / (len(DF_p_vals)) * 100, 3)))
Percent of stationary counties: 86.316%

The percent of counties with stationary timeseries is pretty high, at about 86%. This is not perfect, since we'd ideally want 100% of the timeseries to pass the test, but it shows us that the vast majority are non-stationary. Since this test can be pretty strict, this is likely a lower bound of the percent of counties with stationary timeseries.

To understand how these disgnostics look for individual counties, I print the DF test, residual distributions, and ACF and PACF plots for the 5 sample counties:

In [50]:
# Function for dsiplaying county-level diagnostics
def decomp_stats(decomp):
    DF_Test(decomp.resid[6:-6])
    dist_ts(decomp[6:-6].resid, 'residual series') 
    auto_partial_corr_plot(decomp[6:-6].resid)
In [51]:
decomp_stats(decomp1)
D-F statistic = -4.433291593406838
p-value = 0.00025905152878926926
number of lags used = 0
Critical value at 5% confidence = -2.9512301791166293
Critical value at 10% confidence = -2.614446989619377
In [52]:
decomp_stats(decomp2)
D-F statistic = -4.415592823873974
p-value = 0.0002785291524644849
number of lags used = 0
Critical value at 5% confidence = -2.9512301791166293
Critical value at 10% confidence = -2.614446989619377
In [53]:
decomp_stats(decomp3)
D-F statistic = -6.434580172444922
p-value = 1.665027056032078e-08
number of lags used = 1
Critical value at 5% confidence = -2.954126991123355
Critical value at 10% confidence = -2.6159676124885216
In [54]:
decomp_stats(decomp4)
D-F statistic = -5.303332924481346
p-value = 5.389276315347986e-06
number of lags used = 0
Critical value at 5% confidence = -2.9512301791166293
Critical value at 10% confidence = -2.614446989619377
In [55]:
decomp_stats(decomp5)
D-F statistic = -7.986237190788795
p-value = 2.5445480790804244e-12
number of lags used = 0
Critical value at 5% confidence = -2.9512301791166293
Critical value at 10% confidence = -2.614446989619377

The STL decomposition appears to have done a good job at removing any non-stationary components of the timeseries data. Given the DF statistics and p-values, we can reject the null hypotheses that the residuals are not stationary. Furthermore, the residuals are close to Normally distributed, and the ACF and PACF plots show largely insignificant lags. In a few cases, there are some signfificant lags in the ACF anf PACF plots, but these are not consistent across counties, making it difficult to generalize this behavior for a model.

Given the lack of significant lags across counties, it would be inappropriate to use an ARIMA model on this data. Instead, I will use OLS models with the economic variables I analyzed earlier to build a model to predict the residuals.

OLS Regressions¶

In this section, I test several different OLS regressions to choose the best model for predicting the residuals of the migration flows. Variations of the models include adding county fixed-effects, removing certain economic variables, and using STL decomposition to use the residuals of the exogenous variables in the regressions.

The first step to running this analysis is to reshape the data back into a long format and merge in the economic variables from earlier.

In [56]:
# Reshape data back to long format
long_data = resid_df[6:-6].unstack()
long_data = long_data.reset_index()
long_data.columns = ['countyfips', 'time', 'net_flow_std']
In [57]:
# Reshape seasonal data back to long format
season_data = seasonal_df[6:-6].unstack()
season_data = season_data.reset_index()
season_data.columns = ['countyfips', 'time', 'seasonal_adjustment']
In [58]:
# Reshape trend data back to long format
trend_data = trend_df[6:-6].unstack()
trend_data = trend_data.reset_index()
trend_data.columns = ['countyfips', 'time', 'trend_adjustment']
In [59]:
# Merge seasonal data with residuals
long_data = long_data.merge(season_data, on=['countyfips', 'time'])
long_data = long_data.merge(trend_data, on=['countyfips', 'time'])
In [60]:
# Merge in exogenous variables
long_data = long_data.merge(df_nonmissing.reset_index(), on=['countyfips', 'time'], how='inner')

For this analysis, I z-score the exogenous variables so that they all have unit variance, making it easier to interpret the coefficients. I also generate a lagged variable for each exogenous variable, which I will use in the regressions.

In [61]:
# Z-score and lag each exogenous variable
for var in ['spend_all', 'revenue_all', 'merchants_all', 'emp', 'gps_retail_and_recreation', 'initclaims_rate_regular']:
    
    long_data[var] =  long_data.groupby([long_data['countyfips']])[[var]].apply(zscore)
    county_obs = long_data.groupby(['countyfips']).count()
    
    lag_varname = "l1_" + var
    long_data[lag_varname] = long_data[var].shift()

We know from the exploratory data analysis that the economic variables also have seasonal and trend components, which may move with the seasonal and trend components of the migration flows. Since we are using the OLS model to predict the residuals of the migration flows, it may therefore makes sense to use the residuals of the economic variables as our predictors. The residuals represent when the variables deviate from the seasonal and trend behavior, so this may be more useful in our regressions given we're modeling the seasonal and trend behavior of the migration flows separately.

Therefore, I next perform the STL decomposition on the exogenous variables. I save the residuals of this decomposition to use in the regressions in place of the exogenous variables.

In [ ]:
for var in ['spend_all', 'gps_retail_and_recreation', 'emp', 'revenue_all']:
    
    df_temp = df_nonmissing[['countyfips', 'year', 'month', var, 'time']]
    
    # Reshape data
    df_temp = df_temp.pivot(index=['time'], columns=['countyfips'], values=[var])
    
    # Only use counties with non-missing values
    kept_counties = county_obs[county_obs['year'] == 25]
    counties = df_nonmissing.merge(kept_counties.reset_index()['countyfips'], on='countyfips', how='inner')
    counties = counties['countyfips'].unique()

    # Generate decomposition dataframes
    resid, seasonal, trend = county_STL(df_temp, var, counties=counties)
    
    new_var = var + "_resid"
    
    # Reshape data
    resid_data = resid[6:-6].unstack()
    resid_data = resid_data.reset_index()
    resid_data.columns = ['countyfips', 'time', new_var]
    
    # Merge in residuals
    long_data = long_data.merge(resid_data, on=['countyfips', 'time'], how='outer')
    
In [63]:
for var in ['spend_all_resid', 'revenue_all_resid', 'emp_resid', 'gps_retail_and_recreation_resid']:
    lag_varname = "l1_" + var
    long_data[lag_varname] = long_data[var].shift()

Finally, I divide the data into training and testing data, using September 2021 as the cutoff. This enables me to run the regressions on the training data, then use the testing data to calculate the residuals and compare models.

In [64]:
long_data_train = long_data[long_data['time'] < "2021-09-01"]
long_data_test = long_data[long_data['time'] >= "2021-09-01"]

I build a function to keep track of the model statistics as I run each regression. This will make it easier to compare the results later on.

In [65]:
r2 = []
adj_r2 = []
f_stat = []
f_stat_p = []
rmse = []
model_index = []

# function to keep track of model statistics
def add_model_stats(df, model, model_number=1):
    
    # Scrape statistics from model object
    model_index.append(model_number)
    r2.append(model.rsquared)
    adj_r2.append(model.rsquared_adj)
    f_stat.append(model.fvalue)
    f_stat_p.append(model.f_pvalue)
    
    # Calculate RMSE for testing data
    df = compute_residuals(df, model)
    rmse.append(np.round(np.std(df['resids']), 3))
    
    # Output dataframe with statistics
    model_data = {'r2': r2, 'adj_r2': adj_r2, 'f_stat': f_stat, 'f_stat_p': f_stat_p, 'RMSE': rmse}
    model_stats = pd.DataFrame(model_data, columns=['r2', 'adj_r2', 'f_stat', 'f_stat_p', 'RMSE'], index=model_index)
    
    return model_stats
    

The first model I test uses the 4 primary economic variables I've been considering throughout the project: credit/debit card spending, foot traffic to retail and recreation, employment levels, and small business revenue, all relative to January 2020 levels. I also include a one-hot-encoded variable for each county, which accounts for controls that vary by county but not over time.

In [66]:
# Model with county fixed effects
formula_fe = 'net_flow_std ~  l1_spend_all + l1_gps_retail_and_recreation + l1_emp + l1_revenue_all + C(countyfips)'

model_num = 1
ols_model_fe = smf.ols(formula_fe, data=long_data_train).fit()
model_stats = add_model_stats(long_data_test, ols_model_fe, model_num)
print(ols_model_fe.summary())
                            OLS Regression Results                            
==============================================================================
Dep. Variable:           net_flow_std   R-squared:                       0.036
Model:                            OLS   Adj. R-squared:                 -0.018
Method:                 Least Squares   F-statistic:                    0.6596
Date:                Sat, 17 Dec 2022   Prob (F-statistic):               1.00
Time:                        20:05:40   Log-Likelihood:                -8308.3
No. Observations:               12406   AIC:                         1.793e+04
Df Residuals:                   11749   BIC:                         2.281e+04
Df Model:                         656                                         
Covariance Type:            nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
Intercept                       -0.0285      0.115     -0.249      0.804      -0.253       0.196
C(countyfips)[T.1055]           -0.0633      0.160     -0.396      0.692      -0.377       0.250
C(countyfips)[T.1069]            0.0627      0.160      0.392      0.695      -0.251       0.376
C(countyfips)[T.1073]           -0.0986      0.160     -0.617      0.537      -0.412       0.215
C(countyfips)[T.1081]            0.0659      0.160      0.412      0.680      -0.247       0.379
C(countyfips)[T.1089]           -0.0474      0.160     -0.296      0.767      -0.361       0.266
C(countyfips)[T.1095]            0.0846      0.160      0.529      0.597      -0.229       0.398
C(countyfips)[T.1097]            0.0316      0.160      0.198      0.843      -0.282       0.345
C(countyfips)[T.1101]            0.0498      0.160      0.312      0.755      -0.263       0.363
C(countyfips)[T.1115]            0.0837      0.160      0.523      0.601      -0.230       0.397
C(countyfips)[T.1117]            0.1316      0.160      0.823      0.410      -0.182       0.445
C(countyfips)[T.1125]            0.0482      0.160      0.302      0.763      -0.265       0.361
C(countyfips)[T.2020]            0.0491      0.160      0.307      0.759      -0.264       0.362
C(countyfips)[T.2090]            0.0387      0.160      0.242      0.809      -0.275       0.352
C(countyfips)[T.4005]            0.0162      0.160      0.101      0.919      -0.297       0.329
C(countyfips)[T.4013]           -0.0018      0.160     -0.011      0.991      -0.315       0.311
C(countyfips)[T.4015]            0.0078      0.160      0.049      0.961      -0.305       0.321
C(countyfips)[T.4017]            0.0107      0.160      0.067      0.947      -0.303       0.324
C(countyfips)[T.4019]            0.0067      0.160      0.042      0.967      -0.307       0.320
C(countyfips)[T.4021]           -0.0016      0.160     -0.010      0.992      -0.315       0.312
C(countyfips)[T.4025]            0.0256      0.160      0.160      0.873      -0.288       0.339
C(countyfips)[T.5031]            0.0430      0.160      0.269      0.788      -0.270       0.356
C(countyfips)[T.5045]            0.0088      0.160      0.055      0.956      -0.304       0.322
C(countyfips)[T.5051]            0.0499      0.160      0.312      0.755      -0.263       0.363
C(countyfips)[T.5143]            0.1256      0.160      0.786      0.432      -0.188       0.439
C(countyfips)[T.6001]           -0.1040      0.160     -0.650      0.515      -0.417       0.209
C(countyfips)[T.6007]           -0.0053      0.160     -0.033      0.973      -0.319       0.308
C(countyfips)[T.6013]            0.0119      0.160      0.075      0.941      -0.301       0.325
C(countyfips)[T.6017]            0.0342      0.160      0.214      0.831      -0.279       0.348
C(countyfips)[T.6019]            0.0474      0.160      0.297      0.767      -0.266       0.361
C(countyfips)[T.6023]            0.1248      0.160      0.781      0.435      -0.189       0.438
C(countyfips)[T.6029]            0.0670      0.160      0.419      0.675      -0.246       0.380
C(countyfips)[T.6037]           -0.1151      0.160     -0.720      0.472      -0.428       0.198
C(countyfips)[T.6039]            0.0265      0.160      0.166      0.868      -0.287       0.340
C(countyfips)[T.6041]           -0.0284      0.160     -0.178      0.859      -0.342       0.285
C(countyfips)[T.6045]            0.0902      0.160      0.564      0.572      -0.223       0.403
C(countyfips)[T.6047]            0.1183      0.160      0.740      0.459      -0.195       0.432
C(countyfips)[T.6053]            0.0763      0.160      0.478      0.633      -0.237       0.390
C(countyfips)[T.6059]           -0.0020      0.160     -0.013      0.990      -0.315       0.311
C(countyfips)[T.6061]            0.1042      0.160      0.652      0.515      -0.209       0.417
C(countyfips)[T.6065]            0.0103      0.160      0.065      0.948      -0.303       0.324
C(countyfips)[T.6067]            0.0005      0.160      0.003      0.998      -0.313       0.314
C(countyfips)[T.6069]            0.1140      0.160      0.713      0.476      -0.199       0.427
C(countyfips)[T.6071]            0.0257      0.160      0.161      0.872      -0.288       0.339
C(countyfips)[T.6073]           -0.0604      0.160     -0.378      0.705      -0.374       0.253
C(countyfips)[T.6075]           -0.0792      0.160     -0.495      0.620      -0.392       0.234
C(countyfips)[T.6077]            0.0722      0.160      0.452      0.651      -0.241       0.385
C(countyfips)[T.6081]           -0.1246      0.160     -0.780      0.436      -0.438       0.189
C(countyfips)[T.6083]            0.0310      0.160      0.194      0.846      -0.282       0.344
C(countyfips)[T.6085]           -0.0859      0.160     -0.537      0.591      -0.399       0.227
C(countyfips)[T.6087]            0.0452      0.160      0.283      0.777      -0.268       0.358
C(countyfips)[T.6089]            0.1097      0.160      0.686      0.493      -0.204       0.423
C(countyfips)[T.6095]            0.0464      0.160      0.290      0.772      -0.267       0.360
C(countyfips)[T.6099]            0.0814      0.160      0.509      0.611      -0.232       0.395
C(countyfips)[T.6101]            0.0436      0.160      0.273      0.785      -0.270       0.357
C(countyfips)[T.6107]            0.0653      0.160      0.408      0.683      -0.248       0.379
C(countyfips)[T.6111]            0.0291      0.160      0.182      0.856      -0.284       0.342
C(countyfips)[T.6113]           -0.0030      0.160     -0.019      0.985      -0.316       0.310
C(countyfips)[T.8001]            0.0822      0.160      0.514      0.607      -0.231       0.396
C(countyfips)[T.8005]            0.0255      0.160      0.160      0.873      -0.288       0.339
C(countyfips)[T.8013]            0.0090      0.160      0.056      0.955      -0.304       0.322
C(countyfips)[T.8014]           -0.0153      0.160     -0.096      0.924      -0.329       0.298
C(countyfips)[T.8031]           -0.0752      0.160     -0.470      0.638      -0.388       0.238
C(countyfips)[T.8035]            0.0456      0.160      0.285      0.775      -0.268       0.359
C(countyfips)[T.8037]            0.0442      0.160      0.276      0.782      -0.269       0.357
C(countyfips)[T.8041]           -0.0069      0.160     -0.043      0.966      -0.320       0.306
C(countyfips)[T.8045]            0.0634      0.160      0.397      0.692      -0.250       0.377
C(countyfips)[T.8059]           -0.0507      0.160     -0.317      0.751      -0.364       0.263
C(countyfips)[T.8077]            0.0771      0.160      0.483      0.629      -0.236       0.390
C(countyfips)[T.8101]            0.0156      0.160      0.098      0.922      -0.298       0.329
C(countyfips)[T.8107]            0.0491      0.160      0.307      0.759      -0.264       0.362
C(countyfips)[T.8117]            0.0320      0.160      0.200      0.841      -0.281       0.345
C(countyfips)[T.8123]            0.1008      0.160      0.631      0.528      -0.212       0.414
C(countyfips)[T.9001]            0.0654      0.160      0.409      0.683      -0.248       0.379
C(countyfips)[T.9003]            0.0415      0.160      0.260      0.795      -0.272       0.355
C(countyfips)[T.9005]            0.1049      0.160      0.656      0.512      -0.208       0.418
C(countyfips)[T.9007]            0.0473      0.160      0.296      0.767      -0.266       0.361
C(countyfips)[T.9009]            0.0572      0.160      0.358      0.721      -0.256       0.370
C(countyfips)[T.9011]            0.0308      0.160      0.193      0.847      -0.282       0.344
C(countyfips)[T.9013]            0.0211      0.160      0.132      0.895      -0.292       0.334
C(countyfips)[T.10001]          -0.0029      0.160     -0.018      0.986      -0.316       0.311
C(countyfips)[T.10003]           0.0509      0.160      0.318      0.750      -0.262       0.364
C(countyfips)[T.12001]           0.0120      0.160      0.075      0.940      -0.301       0.325
C(countyfips)[T.12009]          -0.0093      0.160     -0.058      0.953      -0.323       0.304
C(countyfips)[T.12011]           0.0064      0.160      0.040      0.968      -0.307       0.320
C(countyfips)[T.12015]          -0.0036      0.160     -0.023      0.982      -0.317       0.310
C(countyfips)[T.12017]           0.0008      0.160      0.005      0.996      -0.312       0.314
C(countyfips)[T.12019]           0.0362      0.160      0.227      0.821      -0.277       0.349
C(countyfips)[T.12021]           0.0023      0.160      0.015      0.988      -0.311       0.316
C(countyfips)[T.12023]          -0.0498      0.160     -0.312      0.755      -0.363       0.263
C(countyfips)[T.12031]           0.0493      0.160      0.309      0.758      -0.264       0.363
C(countyfips)[T.12033]          -0.0824      0.160     -0.516      0.606      -0.396       0.231
C(countyfips)[T.12035]           0.0207      0.160      0.130      0.897      -0.293       0.334
C(countyfips)[T.12053]           0.0034      0.160      0.021      0.983      -0.310       0.317
C(countyfips)[T.12055]          -0.0073      0.160     -0.046      0.963      -0.321       0.306
C(countyfips)[T.12057]           0.0339      0.160      0.212      0.832      -0.279       0.347
C(countyfips)[T.12061]           0.0023      0.160      0.015      0.988      -0.311       0.316
C(countyfips)[T.12069]           0.0048      0.160      0.030      0.976      -0.308       0.318
C(countyfips)[T.12071]          -0.0002      0.160     -0.001      0.999      -0.313       0.313
C(countyfips)[T.12073]          -0.0224      0.160     -0.140      0.889      -0.336       0.291
C(countyfips)[T.12081]           0.0045      0.160      0.028      0.977      -0.309       0.318
C(countyfips)[T.12083]          -0.0031      0.160     -0.019      0.985      -0.316       0.310
C(countyfips)[T.12085]           0.0072      0.160      0.045      0.964      -0.306       0.320
C(countyfips)[T.12086]          -0.0298      0.160     -0.186      0.852      -0.343       0.283
C(countyfips)[T.12087]           0.0050      0.160      0.032      0.975      -0.308       0.318
C(countyfips)[T.12091]          -0.0023      0.160     -0.014      0.989      -0.315       0.311
C(countyfips)[T.12095]          -0.0517      0.160     -0.324      0.746      -0.365       0.262
C(countyfips)[T.12097]           0.0320      0.160      0.200      0.841      -0.281       0.345
C(countyfips)[T.12099]           0.0035      0.160      0.022      0.983      -0.310       0.317
C(countyfips)[T.12101]           0.0042      0.160      0.026      0.979      -0.309       0.317
C(countyfips)[T.12103]          -0.0044      0.160     -0.028      0.978      -0.318       0.309
C(countyfips)[T.12105]           0.0014      0.160      0.009      0.993      -0.312       0.315
C(countyfips)[T.12107]           0.0602      0.160      0.376      0.707      -0.253       0.374
C(countyfips)[T.12109]           0.0077      0.160      0.048      0.962      -0.306       0.321
C(countyfips)[T.12111]          -0.0069      0.160     -0.043      0.966      -0.320       0.306
C(countyfips)[T.12113]          -0.0272      0.160     -0.170      0.865      -0.340       0.286
C(countyfips)[T.12115]           0.0009      0.160      0.006      0.995      -0.312       0.314
C(countyfips)[T.12117]           0.0628      0.160      0.393      0.694      -0.251       0.376
C(countyfips)[T.12119]           0.0080      0.160      0.050      0.960      -0.305       0.321
C(countyfips)[T.12127]           0.0008      0.160      0.005      0.996      -0.312       0.314
C(countyfips)[T.12131]           0.0086      0.160      0.054      0.957      -0.305       0.322
C(countyfips)[T.13013]          -0.0399      0.160     -0.250      0.803      -0.353       0.273
C(countyfips)[T.13015]           0.0237      0.160      0.148      0.882      -0.290       0.337
C(countyfips)[T.13021]           0.0358      0.160      0.224      0.823      -0.277       0.349
C(countyfips)[T.13031]           0.0319      0.160      0.200      0.842      -0.281       0.345
C(countyfips)[T.13039]           0.0545      0.160      0.341      0.733      -0.259       0.368
C(countyfips)[T.13045]           0.0818      0.160      0.512      0.609      -0.232       0.395
C(countyfips)[T.13051]           0.0727      0.160      0.455      0.649      -0.241       0.386
C(countyfips)[T.13057]           0.0937      0.160      0.586      0.558      -0.220       0.407
C(countyfips)[T.13059]           0.0017      0.160      0.010      0.992      -0.312       0.315
C(countyfips)[T.13063]           0.1204      0.160      0.753      0.451      -0.193       0.434
C(countyfips)[T.13067]           0.0603      0.160      0.377      0.706      -0.253       0.374
C(countyfips)[T.13073]          -0.0449      0.160     -0.281      0.779      -0.358       0.268
C(countyfips)[T.13077]          -0.0291      0.160     -0.182      0.855      -0.342       0.284
C(countyfips)[T.13089]           0.0251      0.160      0.157      0.875      -0.288       0.338
C(countyfips)[T.13095]           0.0248      0.160      0.155      0.877      -0.289       0.338
C(countyfips)[T.13097]          -0.0450      0.160     -0.282      0.778      -0.358       0.268
C(countyfips)[T.13113]           0.0052      0.160      0.033      0.974      -0.308       0.319
C(countyfips)[T.13117]           0.0774      0.160      0.484      0.628      -0.236       0.391
C(countyfips)[T.13121]          -0.0392      0.160     -0.245      0.806      -0.352       0.274
C(countyfips)[T.13129]          -0.1022      0.160     -0.639      0.523      -0.415       0.211
C(countyfips)[T.13135]           0.0466      0.160      0.291      0.771      -0.267       0.360
C(countyfips)[T.13139]           0.0963      0.160      0.602      0.547      -0.217       0.410
C(countyfips)[T.13151]           0.1083      0.160      0.678      0.498      -0.205       0.422
C(countyfips)[T.13153]          -0.0042      0.160     -0.026      0.979      -0.318       0.309
C(countyfips)[T.13179]           0.0255      0.160      0.159      0.873      -0.288       0.339
C(countyfips)[T.13185]           0.0623      0.160      0.390      0.697      -0.251       0.376
C(countyfips)[T.13215]           0.0058      0.160      0.036      0.971      -0.308       0.319
C(countyfips)[T.13217]           0.0752      0.160      0.471      0.638      -0.238       0.389
C(countyfips)[T.13245]          -0.0590      0.160     -0.369      0.712      -0.372       0.254
C(countyfips)[T.13247]           0.0322      0.160      0.201      0.840      -0.281       0.345
C(countyfips)[T.13275]           0.0365      0.160      0.228      0.819      -0.277       0.350
C(countyfips)[T.13297]           0.0456      0.160      0.285      0.775      -0.268       0.359
C(countyfips)[T.13313]          -0.0134      0.160     -0.084      0.933      -0.327       0.300
C(countyfips)[T.15003]           0.0444      0.160      0.278      0.781      -0.269       0.358
C(countyfips)[T.16001]           0.0938      0.160      0.587      0.557      -0.219       0.407
C(countyfips)[T.16005]           0.0123      0.160      0.077      0.938      -0.301       0.326
C(countyfips)[T.16017]           0.0420      0.160      0.263      0.793      -0.271       0.355
C(countyfips)[T.16019]           0.0417      0.160      0.261      0.794      -0.271       0.355
C(countyfips)[T.16027]           0.0962      0.160      0.602      0.547      -0.217       0.409
C(countyfips)[T.16055]           0.0308      0.160      0.193      0.847      -0.283       0.344
C(countyfips)[T.17031]          -0.1100      0.160     -0.688      0.491      -0.423       0.203
C(countyfips)[T.17037]           0.0778      0.160      0.487      0.626      -0.235       0.391
C(countyfips)[T.17043]           0.0172      0.160      0.108      0.914      -0.296       0.330
C(countyfips)[T.17089]           0.0322      0.160      0.202      0.840      -0.281       0.345
C(countyfips)[T.17097]           0.0307      0.160      0.192      0.848      -0.283       0.344
C(countyfips)[T.17099]           0.0579      0.160      0.362      0.717      -0.255       0.371
C(countyfips)[T.17111]           0.0309      0.160      0.193      0.847      -0.282       0.344
C(countyfips)[T.17119]           0.1185      0.160      0.742      0.458      -0.195       0.432
C(countyfips)[T.17143]           0.0581      0.160      0.364      0.716      -0.255       0.371
C(countyfips)[T.17163]           0.0115      0.160      0.072      0.943      -0.302       0.325
C(countyfips)[T.17167]           0.0719      0.160      0.450      0.653      -0.241       0.385
C(countyfips)[T.17183]           0.0528      0.160      0.330      0.741      -0.261       0.366
C(countyfips)[T.17197]           0.0255      0.160      0.160      0.873      -0.288       0.339
C(countyfips)[T.17201]           0.0571      0.160      0.357      0.721      -0.256       0.370
C(countyfips)[T.18003]           0.0716      0.160      0.448      0.654      -0.242       0.385
C(countyfips)[T.18011]           0.0607      0.160      0.380      0.704      -0.253       0.374
C(countyfips)[T.18057]           0.0359      0.160      0.225      0.822      -0.277       0.349
C(countyfips)[T.18063]           0.0373      0.160      0.234      0.815      -0.276       0.351
C(countyfips)[T.18081]           0.0332      0.160      0.208      0.835      -0.280       0.346
C(countyfips)[T.18091]           0.0338      0.160      0.211      0.833      -0.279       0.347
C(countyfips)[T.18097]          -0.0615      0.160     -0.385      0.701      -0.375       0.252
C(countyfips)[T.18127]           0.0640      0.160      0.400      0.689      -0.249       0.377
C(countyfips)[T.18163]           0.0920      0.160      0.576      0.565      -0.221       0.405
C(countyfips)[T.19013]           0.0681      0.160      0.426      0.670      -0.245       0.381
C(countyfips)[T.19061]           0.0038      0.160      0.024      0.981      -0.309       0.317
C(countyfips)[T.19113]           0.0093      0.160      0.058      0.953      -0.304       0.323
C(countyfips)[T.19153]           0.0778      0.160      0.487      0.626      -0.235       0.391
C(countyfips)[T.19155]           0.0033      0.160      0.021      0.983      -0.310       0.317
C(countyfips)[T.19163]           0.0454      0.160      0.284      0.777      -0.268       0.359
C(countyfips)[T.19169]           0.0478      0.160      0.299      0.765      -0.265       0.361
C(countyfips)[T.19193]           0.0978      0.160      0.612      0.541      -0.216       0.411
C(countyfips)[T.20045]           0.0204      0.160      0.128      0.899      -0.293       0.334
C(countyfips)[T.20173]           0.0795      0.160      0.497      0.619      -0.234       0.393
C(countyfips)[T.20209]          -0.0932      0.160     -0.583      0.560      -0.407       0.220
C(countyfips)[T.21015]           0.0497      0.160      0.311      0.756      -0.264       0.363
C(countyfips)[T.21037]          -0.0179      0.160     -0.112      0.911      -0.331       0.295
C(countyfips)[T.21059]           0.0656      0.160      0.410      0.682      -0.248       0.379
C(countyfips)[T.21067]           0.0311      0.160      0.195      0.846      -0.282       0.344
C(countyfips)[T.21111]           0.0119      0.160      0.075      0.941      -0.301       0.325
C(countyfips)[T.21199]           0.0709      0.160      0.444      0.657      -0.242       0.384
C(countyfips)[T.21227]           0.0913      0.160      0.571      0.568      -0.222       0.405
C(countyfips)[T.22005]           0.0483      0.160      0.302      0.762      -0.265       0.362
C(countyfips)[T.22017]           0.0349      0.160      0.218      0.827      -0.278       0.348
C(countyfips)[T.22033]           0.0009      0.160      0.006      0.995      -0.312       0.314
C(countyfips)[T.22051]           0.1033      0.160      0.646      0.518      -0.210       0.417
C(countyfips)[T.22055]           0.0692      0.160      0.433      0.665      -0.244       0.383
C(countyfips)[T.22063]           0.1012      0.160      0.633      0.527      -0.212       0.414
C(countyfips)[T.22071]          -0.0004      0.160     -0.003      0.998      -0.314       0.313
C(countyfips)[T.22073]           0.0820      0.160      0.513      0.608      -0.231       0.395
C(countyfips)[T.22103]           0.1243      0.160      0.778      0.437      -0.189       0.438
C(countyfips)[T.22105]           0.0733      0.160      0.458      0.647      -0.240       0.386
C(countyfips)[T.22109]           0.1610      0.160      1.007      0.314      -0.152       0.474
C(countyfips)[T.23001]           0.0583      0.160      0.365      0.715      -0.255       0.372
C(countyfips)[T.23005]           0.0196      0.160      0.123      0.902      -0.294       0.333
C(countyfips)[T.23019]           0.0432      0.160      0.270      0.787      -0.270       0.357
C(countyfips)[T.24001]           0.1803      0.160      1.128      0.259      -0.133       0.494
C(countyfips)[T.24003]           0.0547      0.160      0.342      0.732      -0.259       0.368
C(countyfips)[T.24005]           0.0378      0.160      0.236      0.813      -0.275       0.351
C(countyfips)[T.24009]           0.0821      0.160      0.514      0.607      -0.231       0.395
C(countyfips)[T.24013]           0.0712      0.160      0.445      0.656      -0.242       0.385
C(countyfips)[T.24017]           0.0420      0.160      0.263      0.793      -0.271       0.355
C(countyfips)[T.24021]           0.0801      0.160      0.501      0.616      -0.233       0.393
C(countyfips)[T.24025]           0.0948      0.160      0.593      0.553      -0.218       0.408
C(countyfips)[T.24027]           0.0669      0.160      0.419      0.675      -0.246       0.380
C(countyfips)[T.24031]          -0.0182      0.160     -0.114      0.909      -0.331       0.295
C(countyfips)[T.24033]          -0.0773      0.160     -0.483      0.629      -0.391       0.236
C(countyfips)[T.24043]           0.0320      0.160      0.200      0.841      -0.281       0.345
C(countyfips)[T.24510]          -0.0149      0.160     -0.093      0.926      -0.328       0.298
C(countyfips)[T.25001]           0.0352      0.160      0.220      0.826      -0.278       0.348
C(countyfips)[T.25003]           0.0606      0.160      0.379      0.705      -0.253       0.374
C(countyfips)[T.25017]          -0.0336      0.160     -0.210      0.833      -0.347       0.280
C(countyfips)[T.25021]           0.0043      0.160      0.027      0.979      -0.309       0.318
C(countyfips)[T.25023]           0.0389      0.160      0.244      0.808      -0.274       0.352
C(countyfips)[T.25025]          -0.0810      0.160     -0.507      0.612      -0.394       0.232
C(countyfips)[T.25027]           0.0566      0.160      0.354      0.723      -0.257       0.370
C(countyfips)[T.26045]           0.0469      0.160      0.293      0.769      -0.266       0.360
C(countyfips)[T.26049]           0.0718      0.160      0.449      0.653      -0.241       0.385
C(countyfips)[T.26065]           0.0342      0.160      0.214      0.831      -0.279       0.347
C(countyfips)[T.26077]           0.0260      0.160      0.163      0.871      -0.287       0.339
C(countyfips)[T.26081]           0.0264      0.160      0.165      0.869      -0.287       0.340
C(countyfips)[T.26099]           0.0286      0.160      0.179      0.858      -0.285       0.342
C(countyfips)[T.26121]           0.0216      0.160      0.135      0.892      -0.292       0.335
C(countyfips)[T.26125]           0.0353      0.160      0.221      0.825      -0.278       0.348
C(countyfips)[T.26139]           0.0182      0.160      0.114      0.910      -0.295       0.331
C(countyfips)[T.26145]           0.0460      0.160      0.288      0.773      -0.267       0.359
C(countyfips)[T.26147]           0.0186      0.160      0.116      0.907      -0.295       0.332
C(countyfips)[T.26161]           0.0397      0.160      0.248      0.804      -0.274       0.353
C(countyfips)[T.26163]           0.0132      0.160      0.083      0.934      -0.300       0.326
C(countyfips)[T.27003]           0.0323      0.160      0.202      0.840      -0.281       0.346
C(countyfips)[T.27005]           0.0205      0.160      0.128      0.898      -0.293       0.334
C(countyfips)[T.27013]           0.0037      0.160      0.023      0.981      -0.310       0.317
C(countyfips)[T.27019]          -0.0189      0.160     -0.118      0.906      -0.332       0.294
C(countyfips)[T.27025]           0.0368      0.160      0.230      0.818      -0.277       0.350
C(countyfips)[T.27035]           0.0448      0.160      0.280      0.779      -0.268       0.358
C(countyfips)[T.27037]           0.0234      0.160      0.146      0.884      -0.290       0.337
C(countyfips)[T.27053]          -0.0027      0.160     -0.017      0.986      -0.316       0.310
C(countyfips)[T.27109]           0.0671      0.160      0.420      0.674      -0.246       0.380
C(countyfips)[T.27123]           0.0017      0.160      0.011      0.992      -0.312       0.315
C(countyfips)[T.27131]           0.0581      0.160      0.363      0.716      -0.255       0.371
C(countyfips)[T.27137]           0.0370      0.160      0.231      0.817      -0.276       0.350
C(countyfips)[T.27139]           0.0578      0.160      0.361      0.718      -0.256       0.371
C(countyfips)[T.27145]           0.0563      0.160      0.353      0.724      -0.257       0.370
C(countyfips)[T.27163]           0.0276      0.160      0.172      0.863      -0.286       0.341
C(countyfips)[T.27171]           0.0613      0.160      0.383      0.701      -0.252       0.375
C(countyfips)[T.28033]           0.0839      0.160      0.525      0.599      -0.229       0.397
C(countyfips)[T.28047]           0.0558      0.160      0.349      0.727      -0.257       0.369
C(countyfips)[T.28049]           0.0179      0.160      0.112      0.911      -0.295       0.331
C(countyfips)[T.28059]           0.1010      0.160      0.632      0.527      -0.212       0.414
C(countyfips)[T.28089]           0.0666      0.160      0.417      0.677      -0.247       0.380
C(countyfips)[T.28121]          -0.0699      0.160     -0.437      0.662      -0.383       0.243
C(countyfips)[T.29019]          -0.0245      0.160     -0.153      0.878      -0.338       0.289
C(countyfips)[T.29021]           0.0978      0.160      0.612      0.541      -0.215       0.411
C(countyfips)[T.29029]           0.0323      0.160      0.202      0.840      -0.281       0.346
C(countyfips)[T.29031]           0.0743      0.160      0.465      0.642      -0.239       0.388
C(countyfips)[T.29047]          -0.0212      0.160     -0.133      0.894      -0.335       0.292
C(countyfips)[T.29071]           0.0233      0.160      0.146      0.884      -0.290       0.336
C(countyfips)[T.29077]           0.0243      0.160      0.152      0.879      -0.289       0.338
C(countyfips)[T.29095]           0.0096      0.160      0.060      0.952      -0.304       0.323
C(countyfips)[T.29097]           0.0282      0.160      0.176      0.860      -0.285       0.341
C(countyfips)[T.29099]           0.0395      0.160      0.247      0.805      -0.274       0.353
C(countyfips)[T.29145]           0.0578      0.160      0.362      0.718      -0.255       0.371
C(countyfips)[T.29183]           0.0552      0.160      0.345      0.730      -0.258       0.368
C(countyfips)[T.29189]           0.0074      0.160      0.046      0.963      -0.306       0.321
C(countyfips)[T.29510]          -0.0802      0.160     -0.502      0.616      -0.393       0.233
C(countyfips)[T.30029]           0.0300      0.160      0.188      0.851      -0.283       0.343
C(countyfips)[T.30049]           0.0418      0.160      0.262      0.793      -0.271       0.355
C(countyfips)[T.30063]           0.0495      0.160      0.310      0.757      -0.264       0.363
C(countyfips)[T.30111]           0.0593      0.160      0.371      0.710      -0.254       0.373
C(countyfips)[T.31019]           0.0951      0.160      0.595      0.552      -0.218       0.408
C(countyfips)[T.31055]           0.0046      0.160      0.029      0.977      -0.309       0.318
C(countyfips)[T.31079]           0.0031      0.160      0.019      0.985      -0.310       0.316
C(countyfips)[T.31109]           0.0082      0.160      0.051      0.959      -0.305       0.322
C(countyfips)[T.31153]           0.0342      0.160      0.214      0.830      -0.279       0.348
C(countyfips)[T.32003]           0.0095      0.160      0.060      0.952      -0.304       0.323
C(countyfips)[T.32005]           0.1133      0.160      0.709      0.478      -0.200       0.427
C(countyfips)[T.32031]           0.1046      0.160      0.655      0.513      -0.209       0.418
C(countyfips)[T.32510]           0.0508      0.160      0.318      0.751      -0.262       0.364
C(countyfips)[T.33001]           0.0202      0.160      0.126      0.899      -0.293       0.333
C(countyfips)[T.33003]           0.0287      0.160      0.180      0.857      -0.285       0.342
C(countyfips)[T.33005]           0.0070      0.160      0.044      0.965      -0.306       0.320
C(countyfips)[T.33011]           0.0525      0.160      0.328      0.743      -0.261       0.366
C(countyfips)[T.33015]           0.0396      0.160      0.248      0.804      -0.274       0.353
C(countyfips)[T.33017]           0.0053      0.160      0.033      0.974      -0.308       0.318
C(countyfips)[T.34001]           0.0242      0.160      0.151      0.880      -0.289       0.337
C(countyfips)[T.34003]           0.0194      0.160      0.121      0.904      -0.294       0.333
C(countyfips)[T.34009]           0.0314      0.160      0.196      0.844      -0.282       0.345
C(countyfips)[T.34011]           0.0251      0.160      0.157      0.875      -0.288       0.338
C(countyfips)[T.34015]           0.0117      0.160      0.073      0.942      -0.302       0.325
C(countyfips)[T.34017]          -0.1268      0.160     -0.794      0.427      -0.440       0.186
C(countyfips)[T.34019]           0.0721      0.160      0.451      0.652      -0.241       0.385
C(countyfips)[T.34021]           0.0332      0.160      0.208      0.836      -0.280       0.346
C(countyfips)[T.34023]           0.0060      0.160      0.038      0.970      -0.307       0.319
C(countyfips)[T.34025]           0.0297      0.160      0.186      0.852      -0.284       0.343
C(countyfips)[T.34027]           0.0489      0.160      0.306      0.759      -0.264       0.362
C(countyfips)[T.34029]           0.0357      0.160      0.223      0.823      -0.278       0.349
C(countyfips)[T.34031]          -0.0748      0.160     -0.468      0.640      -0.388       0.238
C(countyfips)[T.34035]           0.0495      0.160      0.310      0.757      -0.264       0.363
C(countyfips)[T.34037]           0.0443      0.160      0.277      0.782      -0.269       0.357
C(countyfips)[T.34039]          -0.0440      0.160     -0.275      0.783      -0.357       0.269
C(countyfips)[T.35001]           0.0044      0.160      0.028      0.978      -0.309       0.318
C(countyfips)[T.35013]           0.0020      0.160      0.012      0.990      -0.311       0.315
C(countyfips)[T.35045]           0.0291      0.160      0.182      0.856      -0.284       0.342
C(countyfips)[T.35049]          -0.0076      0.160     -0.048      0.962      -0.321       0.306
C(countyfips)[T.35055]           0.0302      0.160      0.189      0.850      -0.283       0.343
C(countyfips)[T.36009]           0.0359      0.160      0.224      0.822      -0.277       0.349
C(countyfips)[T.36013]           0.0281      0.160      0.176      0.861      -0.285       0.341
C(countyfips)[T.36015]           0.0432      0.160      0.270      0.787      -0.270       0.356
C(countyfips)[T.36019]           0.0422      0.160      0.264      0.792      -0.271       0.355
C(countyfips)[T.36027]           0.0769      0.160      0.481      0.630      -0.236       0.390
C(countyfips)[T.36029]           0.0234      0.160      0.147      0.884      -0.290       0.337
C(countyfips)[T.36035]           0.0376      0.160      0.235      0.814      -0.276       0.351
C(countyfips)[T.36039]           0.0490      0.160      0.306      0.759      -0.264       0.362
C(countyfips)[T.36043]           0.0191      0.160      0.119      0.905      -0.294       0.332
C(countyfips)[T.36045]           0.0052      0.160      0.033      0.974      -0.308       0.319
C(countyfips)[T.36051]       -9.872e-05      0.160     -0.001      1.000      -0.313       0.313
C(countyfips)[T.36053]           0.0337      0.160      0.211      0.833      -0.280       0.347
C(countyfips)[T.36055]           0.0307      0.160      0.192      0.848      -0.283       0.344
C(countyfips)[T.36059]           0.0184      0.160      0.115      0.908      -0.295       0.332
C(countyfips)[T.36061]          -0.0945      0.160     -0.592      0.554      -0.408       0.219
C(countyfips)[T.36063]           0.0452      0.160      0.283      0.777      -0.268       0.358
C(countyfips)[T.36065]           0.0325      0.160      0.203      0.839      -0.281       0.346
C(countyfips)[T.36067]           0.0503      0.160      0.315      0.753      -0.263       0.363
C(countyfips)[T.36069]           0.0245      0.160      0.154      0.878      -0.289       0.338
C(countyfips)[T.36071]           0.0558      0.160      0.349      0.727      -0.257       0.369
C(countyfips)[T.36075]           0.0451      0.160      0.282      0.778      -0.268       0.358
C(countyfips)[T.36077]           0.0547      0.160      0.342      0.732      -0.259       0.368
C(countyfips)[T.36079]           0.0730      0.160      0.457      0.648      -0.240       0.386
C(countyfips)[T.36081]          -0.1060      0.160     -0.663      0.507      -0.419       0.207
C(countyfips)[T.36085]          -0.0136      0.160     -0.085      0.932      -0.327       0.300
C(countyfips)[T.36087]           0.0190      0.160      0.119      0.905      -0.294       0.332
C(countyfips)[T.36089]           0.0567      0.160      0.355      0.723      -0.257       0.370
C(countyfips)[T.36091]           0.0390      0.160      0.244      0.807      -0.274       0.352
C(countyfips)[T.36093]           0.0470      0.160      0.294      0.769      -0.266       0.360
C(countyfips)[T.36101]           0.0435      0.160      0.272      0.785      -0.270       0.357
C(countyfips)[T.36103]           0.0604      0.160      0.378      0.705      -0.253       0.374
C(countyfips)[T.36105]           0.0524      0.160      0.328      0.743      -0.261       0.366
C(countyfips)[T.36111]           0.0883      0.160      0.553      0.580      -0.225       0.402
C(countyfips)[T.36113]           0.0174      0.160      0.109      0.913      -0.296       0.331
C(countyfips)[T.36119]           0.0117      0.160      0.073      0.942      -0.302       0.325
C(countyfips)[T.37001]           0.0037      0.160      0.023      0.981      -0.310       0.317
C(countyfips)[T.37019]           0.1069      0.160      0.669      0.504      -0.206       0.420
C(countyfips)[T.37021]           0.0743      0.160      0.465      0.642      -0.239       0.388
C(countyfips)[T.37025]           0.0446      0.160      0.279      0.780      -0.269       0.358
C(countyfips)[T.37027]           0.1027      0.160      0.643      0.520      -0.211       0.416
C(countyfips)[T.37031]           0.0987      0.160      0.618      0.537      -0.215       0.412
C(countyfips)[T.37035]           0.0435      0.160      0.272      0.785      -0.270       0.357
C(countyfips)[T.37037]           0.0661      0.160      0.413      0.679      -0.247       0.379
C(countyfips)[T.37045]           0.0559      0.160      0.350      0.727      -0.257       0.369
C(countyfips)[T.37047]          -0.0701      0.160     -0.438      0.661      -0.383       0.243
C(countyfips)[T.37049]           0.0504      0.160      0.315      0.753      -0.263       0.364
C(countyfips)[T.37051]           0.0062      0.160      0.039      0.969      -0.307       0.319
C(countyfips)[T.37055]           0.0856      0.160      0.536      0.592      -0.228       0.399
C(countyfips)[T.37057]           0.0904      0.160      0.566      0.571      -0.223       0.404
C(countyfips)[T.37059]           0.0941      0.160      0.589      0.556      -0.219       0.407
C(countyfips)[T.37063]          -0.0171      0.160     -0.107      0.915      -0.330       0.296
C(countyfips)[T.37067]           0.0851      0.160      0.533      0.594      -0.228       0.398
C(countyfips)[T.37071]           0.0225      0.160      0.140      0.888      -0.291       0.336
C(countyfips)[T.37081]           0.0145      0.160      0.091      0.928      -0.299       0.328
C(countyfips)[T.37085]           0.0134      0.160      0.084      0.933      -0.300       0.327
C(countyfips)[T.37087]           0.0182      0.160      0.114      0.909      -0.295       0.332
C(countyfips)[T.37089]           0.0459      0.160      0.287      0.774      -0.267       0.359
C(countyfips)[T.37097]           0.0272      0.160      0.170      0.865      -0.286       0.340
C(countyfips)[T.37101]           0.0779      0.160      0.488      0.626      -0.235       0.391
C(countyfips)[T.37105]           0.0754      0.160      0.472      0.637      -0.238       0.389
C(countyfips)[T.37109]           0.0814      0.160      0.510      0.610      -0.232       0.395
C(countyfips)[T.37119]           0.0613      0.160      0.384      0.701      -0.252       0.375
C(countyfips)[T.37125]           0.0496      0.160      0.310      0.756      -0.264       0.363
C(countyfips)[T.37127]          -0.0417      0.160     -0.261      0.794      -0.355       0.271
C(countyfips)[T.37129]           0.0552      0.160      0.346      0.730      -0.258       0.369
C(countyfips)[T.37133]           0.0735      0.160      0.460      0.646      -0.240       0.387
C(countyfips)[T.37135]           0.0050      0.160      0.031      0.975      -0.308       0.318
C(countyfips)[T.37139]          -0.0345      0.160     -0.216      0.829      -0.348       0.279
C(countyfips)[T.37147]          -0.0381      0.160     -0.238      0.812      -0.351       0.275
C(countyfips)[T.37151]          -0.0066      0.160     -0.041      0.967      -0.320       0.307
C(countyfips)[T.37155]           0.0319      0.160      0.200      0.842      -0.281       0.345
C(countyfips)[T.37157]          -0.0257      0.160     -0.161      0.872      -0.339       0.288
C(countyfips)[T.37159]           0.0686      0.160      0.429      0.668      -0.245       0.382
C(countyfips)[T.37161]          -0.0002      0.160     -0.001      0.999      -0.313       0.313
C(countyfips)[T.37163]           0.0455      0.160      0.284      0.776      -0.268       0.359
C(countyfips)[T.37167]           0.0298      0.160      0.187      0.852      -0.283       0.343
C(countyfips)[T.37169]          -0.0008      0.160     -0.005      0.996      -0.314       0.312
C(countyfips)[T.37179]          -0.0175      0.160     -0.109      0.913      -0.331       0.296
C(countyfips)[T.37183]           0.1276      0.160      0.799      0.425      -0.186       0.441
C(countyfips)[T.37189]           0.0256      0.160      0.160      0.873      -0.288       0.339
C(countyfips)[T.37191]           0.0036      0.160      0.023      0.982      -0.310       0.317
C(countyfips)[T.37193]           0.0654      0.160      0.409      0.682      -0.248       0.379
C(countyfips)[T.37195]          -0.0312      0.160     -0.195      0.845      -0.344       0.282
C(countyfips)[T.38017]           0.0408      0.160      0.255      0.799      -0.272       0.354
C(countyfips)[T.38035]           0.0067      0.160      0.042      0.967      -0.307       0.320
C(countyfips)[T.39017]           0.0339      0.160      0.212      0.832      -0.279       0.347
C(countyfips)[T.39025]           0.0554      0.160      0.347      0.729      -0.258       0.369
C(countyfips)[T.39035]           0.0037      0.160      0.023      0.982      -0.310       0.317
C(countyfips)[T.39041]           0.0366      0.160      0.229      0.819      -0.277       0.350
C(countyfips)[T.39043]           0.0529      0.160      0.331      0.741      -0.260       0.366
C(countyfips)[T.39045]           0.0271      0.160      0.170      0.865      -0.286       0.340
C(countyfips)[T.39049]           0.0424      0.160      0.265      0.791      -0.271       0.356
C(countyfips)[T.39055]           0.0642      0.160      0.402      0.688      -0.249       0.377
C(countyfips)[T.39057]           0.0627      0.160      0.392      0.695      -0.251       0.376
C(countyfips)[T.39061]          -0.0380      0.160     -0.238      0.812      -0.351       0.275
C(countyfips)[T.39085]           0.0479      0.160      0.300      0.764      -0.265       0.361
C(countyfips)[T.39089]           0.0223      0.160      0.140      0.889      -0.291       0.336
C(countyfips)[T.39093]           0.0449      0.160      0.281      0.779      -0.268       0.358
C(countyfips)[T.39095]           0.0115      0.160      0.072      0.943      -0.302       0.325
C(countyfips)[T.39099]           0.0644      0.160      0.403      0.687      -0.249       0.378
C(countyfips)[T.39103]           0.0146      0.160      0.092      0.927      -0.299       0.328
C(countyfips)[T.39109]           0.0747      0.160      0.467      0.640      -0.239       0.388
C(countyfips)[T.39113]           0.0255      0.160      0.159      0.873      -0.288       0.339
C(countyfips)[T.39119]           0.0434      0.160      0.271      0.786      -0.270       0.357
C(countyfips)[T.39123]           0.0626      0.160      0.392      0.695      -0.251       0.376
C(countyfips)[T.39133]           0.0640      0.160      0.400      0.689      -0.249       0.377
C(countyfips)[T.39147]           0.0444      0.160      0.278      0.781      -0.269       0.358
C(countyfips)[T.39151]           0.0927      0.160      0.580      0.562      -0.221       0.406
C(countyfips)[T.39153]           0.0111      0.160      0.070      0.945      -0.302       0.324
C(countyfips)[T.39155]           0.0969      0.160      0.606      0.544      -0.216       0.410
C(countyfips)[T.39157]           0.0900      0.160      0.563      0.573      -0.223       0.403
C(countyfips)[T.39165]           0.0357      0.160      0.223      0.823      -0.278       0.349
C(countyfips)[T.39169]           0.0086      0.160      0.054      0.957      -0.305       0.322
C(countyfips)[T.40031]           0.1010      0.160      0.632      0.527      -0.212       0.414
C(countyfips)[T.40119]           0.0120      0.160      0.075      0.940      -0.301       0.325
C(countyfips)[T.40143]          -0.0194      0.160     -0.122      0.903      -0.333       0.294
C(countyfips)[T.41005]           0.0338      0.160      0.212      0.832      -0.279       0.347
C(countyfips)[T.41007]           0.0581      0.160      0.364      0.716      -0.255       0.371
C(countyfips)[T.41011]           0.1221      0.160      0.764      0.445      -0.191       0.435
C(countyfips)[T.41017]           0.0732      0.160      0.458      0.647      -0.240       0.386
C(countyfips)[T.41019]           0.0957      0.160      0.599      0.549      -0.218       0.409
C(countyfips)[T.41029]          -0.0337      0.160     -0.211      0.833      -0.347       0.280
C(countyfips)[T.41033]           0.0707      0.160      0.442      0.658      -0.243       0.384
C(countyfips)[T.41035]           0.0556      0.160      0.348      0.728      -0.258       0.369
C(countyfips)[T.41039]           0.0291      0.160      0.182      0.856      -0.284       0.342
C(countyfips)[T.41041]           0.0300      0.160      0.188      0.851      -0.283       0.343
C(countyfips)[T.41043]           0.0420      0.160      0.263      0.793      -0.271       0.355
C(countyfips)[T.41047]           0.0732      0.160      0.458      0.647      -0.240       0.387
C(countyfips)[T.41051]          -0.0570      0.160     -0.357      0.721      -0.370       0.256
C(countyfips)[T.41059]          -0.0253      0.160     -0.158      0.874      -0.339       0.288
C(countyfips)[T.41067]           0.0344      0.160      0.215      0.830      -0.279       0.348
C(countyfips)[T.42003]           0.0028      0.160      0.018      0.986      -0.310       0.316
C(countyfips)[T.42007]           0.0740      0.160      0.463      0.643      -0.239       0.387
C(countyfips)[T.42011]           0.0194      0.160      0.121      0.903      -0.294       0.333
C(countyfips)[T.42013]           0.0711      0.160      0.445      0.656      -0.242       0.384
C(countyfips)[T.42015]           0.0670      0.160      0.419      0.675      -0.246       0.380
C(countyfips)[T.42017]           0.0473      0.160      0.296      0.767      -0.266       0.361
C(countyfips)[T.42019]           0.0422      0.160      0.264      0.792      -0.271       0.355
C(countyfips)[T.42021]           0.0457      0.160      0.286      0.775      -0.268       0.359
C(countyfips)[T.42027]           0.0160      0.160      0.100      0.920      -0.297       0.329
C(countyfips)[T.42029]           0.1057      0.160      0.661      0.508      -0.208       0.419
C(countyfips)[T.42033]           0.0472      0.160      0.295      0.768      -0.266       0.361
C(countyfips)[T.42041]           0.0848      0.160      0.530      0.596      -0.228       0.398
C(countyfips)[T.42043]           0.0375      0.160      0.235      0.814      -0.276       0.351
C(countyfips)[T.42045]           0.0263      0.160      0.165      0.869      -0.287       0.340
C(countyfips)[T.42049]           0.0374      0.160      0.234      0.815      -0.276       0.351
C(countyfips)[T.42051]           0.0302      0.160      0.189      0.850      -0.283       0.343
C(countyfips)[T.42055]           0.0985      0.160      0.616      0.538      -0.215       0.412
C(countyfips)[T.42063]           0.0648      0.160      0.405      0.685      -0.249       0.378
C(countyfips)[T.42065]           0.0466      0.160      0.292      0.771      -0.267       0.360
C(countyfips)[T.42069]           0.0259      0.160      0.162      0.871      -0.287       0.339
C(countyfips)[T.42071]           0.0406      0.160      0.254      0.799      -0.273       0.354
C(countyfips)[T.42073]           0.0130      0.160      0.081      0.935      -0.300       0.326
C(countyfips)[T.42075]          -0.0099      0.160     -0.062      0.950      -0.323       0.303
C(countyfips)[T.42077]           0.0562      0.160      0.351      0.725      -0.257       0.369
C(countyfips)[T.42079]           0.0099      0.160      0.062      0.951      -0.303       0.323
C(countyfips)[T.42085]           0.0492      0.160      0.308      0.758      -0.264       0.363
C(countyfips)[T.42089]           0.0731      0.160      0.458      0.647      -0.240       0.386
C(countyfips)[T.42091]           0.0355      0.160      0.222      0.824      -0.278       0.349
C(countyfips)[T.42095]           0.0490      0.160      0.306      0.759      -0.264       0.362
C(countyfips)[T.42097]           0.0491      0.160      0.307      0.759      -0.264       0.362
C(countyfips)[T.42103]           0.0333      0.160      0.208      0.835      -0.280       0.347
C(countyfips)[T.42115]           0.0645      0.160      0.403      0.687      -0.249       0.378
C(countyfips)[T.42125]           0.0558      0.160      0.349      0.727      -0.257       0.369
C(countyfips)[T.42129]           0.0571      0.160      0.357      0.721      -0.256       0.370
C(countyfips)[T.42133]           0.0634      0.160      0.397      0.692      -0.250       0.377
C(countyfips)[T.44003]           0.0414      0.160      0.259      0.795      -0.272       0.355
C(countyfips)[T.44007]           0.0226      0.160      0.141      0.888      -0.291       0.336
C(countyfips)[T.44009]           0.0298      0.160      0.187      0.852      -0.283       0.343
C(countyfips)[T.45003]           0.0366      0.160      0.229      0.819      -0.277       0.350
C(countyfips)[T.45007]           0.0794      0.160      0.497      0.619      -0.234       0.393
C(countyfips)[T.45015]           0.0628      0.160      0.393      0.694      -0.250       0.376
C(countyfips)[T.45019]           0.0501      0.160      0.313      0.754      -0.263       0.363
C(countyfips)[T.45035]           0.0404      0.160      0.253      0.800      -0.273       0.354
C(countyfips)[T.45043]           0.0682      0.160      0.427      0.670      -0.245       0.382
C(countyfips)[T.45045]           0.0676      0.160      0.423      0.672      -0.246       0.381
C(countyfips)[T.45051]           0.0245      0.160      0.153      0.878      -0.289       0.338
C(countyfips)[T.45057]           0.1235      0.160      0.773      0.440      -0.190       0.437
C(countyfips)[T.45063]          -0.0279      0.160     -0.175      0.861      -0.341       0.285
C(countyfips)[T.45077]          -0.0026      0.160     -0.016      0.987      -0.316       0.311
C(countyfips)[T.45079]           0.1001      0.160      0.626      0.531      -0.213       0.413
C(countyfips)[T.45083]          -0.0087      0.160     -0.054      0.957      -0.322       0.305
C(countyfips)[T.45085]           0.0379      0.160      0.237      0.812      -0.275       0.351
C(countyfips)[T.45091]          -0.0342      0.160     -0.214      0.830      -0.347       0.279
C(countyfips)[T.46099]           0.0598      0.160      0.374      0.708      -0.253       0.373
C(countyfips)[T.46103]           0.0306      0.160      0.192      0.848      -0.283       0.344
C(countyfips)[T.47001]          -0.0024      0.160     -0.015      0.988      -0.316       0.311
C(countyfips)[T.47009]           0.1390      0.160      0.870      0.384      -0.174       0.452
C(countyfips)[T.47011]           0.0941      0.160      0.589      0.556      -0.219       0.407
C(countyfips)[T.47037]          -0.0137      0.160     -0.086      0.931      -0.327       0.299
C(countyfips)[T.47043]           0.1098      0.160      0.687      0.492      -0.203       0.423
C(countyfips)[T.47065]          -0.0088      0.160     -0.055      0.956      -0.322       0.304
C(countyfips)[T.47093]           0.0566      0.160      0.354      0.723      -0.257       0.370
C(countyfips)[T.47113]           0.0143      0.160      0.090      0.929      -0.299       0.328
C(countyfips)[T.47141]           0.0945      0.160      0.592      0.554      -0.219       0.408
C(countyfips)[T.47149]          -0.0005      0.160     -0.003      0.997      -0.314       0.313
C(countyfips)[T.47155]           0.1372      0.160      0.859      0.390      -0.176       0.450
C(countyfips)[T.47157]          -0.0335      0.160     -0.209      0.834      -0.347       0.280
C(countyfips)[T.47163]           0.1053      0.160      0.659      0.510      -0.208       0.418
C(countyfips)[T.47165]           0.0718      0.160      0.450      0.653      -0.241       0.385
C(countyfips)[T.47179]           0.0828      0.160      0.518      0.604      -0.230       0.396
C(countyfips)[T.47187]           0.0641      0.160      0.401      0.688      -0.249       0.377
C(countyfips)[T.47189]           0.0360      0.160      0.225      0.822      -0.277       0.349
C(countyfips)[T.48013]           0.0126      0.160      0.079      0.937      -0.301       0.326
C(countyfips)[T.48021]           0.0808      0.160      0.506      0.613      -0.232       0.394
C(countyfips)[T.48027]           0.0793      0.160      0.496      0.620      -0.234       0.392
C(countyfips)[T.48029]           0.0772      0.160      0.483      0.629      -0.236       0.390
C(countyfips)[T.48039]          -0.0412      0.160     -0.258      0.797      -0.354       0.272
C(countyfips)[T.48041]           0.0176      0.160      0.110      0.912      -0.296       0.331
C(countyfips)[T.48061]           0.0010      0.160      0.006      0.995      -0.312       0.314
C(countyfips)[T.48085]           0.1124      0.160      0.703      0.482      -0.201       0.426
C(countyfips)[T.48091]           0.0149      0.160      0.093      0.926      -0.298       0.328
C(countyfips)[T.48113]          -0.0059      0.160     -0.037      0.971      -0.319       0.307
C(countyfips)[T.48121]           0.0662      0.160      0.415      0.678      -0.247       0.380
C(countyfips)[T.48139]           0.0505      0.160      0.316      0.752      -0.263       0.364
C(countyfips)[T.48141]           0.0187      0.160      0.117      0.907      -0.295       0.332
C(countyfips)[T.48157]           0.0947      0.160      0.593      0.553      -0.219       0.408
C(countyfips)[T.48167]          -0.0004      0.160     -0.002      0.998      -0.314       0.313
C(countyfips)[T.48171]           0.1065      0.160      0.667      0.505      -0.207       0.420
C(countyfips)[T.48181]           0.0942      0.160      0.589      0.556      -0.219       0.408
C(countyfips)[T.48183]           0.0978      0.160      0.612      0.541      -0.215       0.411
C(countyfips)[T.48187]          -0.0118      0.160     -0.074      0.941      -0.325       0.301
C(countyfips)[T.48201]          -0.0387      0.160     -0.242      0.808      -0.352       0.275
C(countyfips)[T.48209]           0.0443      0.160      0.277      0.782      -0.269       0.358
C(countyfips)[T.48215]          -0.0128      0.160     -0.080      0.936      -0.326       0.300
C(countyfips)[T.48221]          -0.0771      0.160     -0.482      0.630      -0.390       0.236
C(countyfips)[T.48231]           0.0216      0.160      0.135      0.892      -0.292       0.335
C(countyfips)[T.48245]          -0.0324      0.160     -0.203      0.839      -0.346       0.281
C(countyfips)[T.48251]           0.1202      0.160      0.752      0.452      -0.193       0.433
C(countyfips)[T.48257]           0.0761      0.160      0.476      0.634      -0.237       0.389
C(countyfips)[T.48265]           0.0103      0.160      0.065      0.949      -0.303       0.324
C(countyfips)[T.48291]           0.0716      0.160      0.448      0.654      -0.242       0.385
C(countyfips)[T.48303]           0.0074      0.160      0.046      0.963      -0.306       0.321
C(countyfips)[T.48309]           0.0415      0.160      0.260      0.795      -0.272       0.355
C(countyfips)[T.48329]          -0.0045      0.160     -0.028      0.978      -0.318       0.309
C(countyfips)[T.48339]           0.0654      0.160      0.409      0.682      -0.248       0.379
C(countyfips)[T.48355]          -0.0154      0.160     -0.097      0.923      -0.329       0.298
C(countyfips)[T.48367]           0.0610      0.160      0.381      0.703      -0.252       0.374
C(countyfips)[T.48375]           0.0653      0.160      0.409      0.683      -0.248       0.379
C(countyfips)[T.48381]           0.0011      0.160      0.007      0.995      -0.312       0.314
C(countyfips)[T.48397]           0.0873      0.160      0.546      0.585      -0.226       0.401
C(countyfips)[T.48423]           0.0273      0.160      0.171      0.864      -0.286       0.341
C(countyfips)[T.48439]          -0.0380      0.160     -0.238      0.812      -0.351       0.275
C(countyfips)[T.48451]          -0.0184      0.160     -0.115      0.908      -0.332       0.295
C(countyfips)[T.48453]          -0.0115      0.160     -0.072      0.943      -0.325       0.302
C(countyfips)[T.48469]           0.0600      0.160      0.375      0.707      -0.253       0.373
C(countyfips)[T.48471]           0.0150      0.160      0.094      0.925      -0.298       0.328
C(countyfips)[T.48479]          -0.0096      0.160     -0.060      0.952      -0.323       0.304
C(countyfips)[T.48485]           0.0451      0.160      0.282      0.778      -0.268       0.358
C(countyfips)[T.48491]           0.0513      0.160      0.321      0.748      -0.262       0.365
C(countyfips)[T.49005]           0.0343      0.160      0.215      0.830      -0.279       0.348
C(countyfips)[T.49035]           0.0510      0.160      0.319      0.750      -0.262       0.364
C(countyfips)[T.49043]           0.0520      0.160      0.325      0.745      -0.261       0.365
C(countyfips)[T.49045]           0.0801      0.160      0.501      0.616      -0.233       0.393
C(countyfips)[T.49049]           0.0834      0.160      0.522      0.602      -0.230       0.397
C(countyfips)[T.49057]           0.0983      0.160      0.615      0.538      -0.215       0.412
C(countyfips)[T.50021]           0.0380      0.160      0.238      0.812      -0.275       0.351
C(countyfips)[T.50025]           0.0758      0.160      0.474      0.635      -0.237       0.389
C(countyfips)[T.51003]           0.0591      0.160      0.370      0.711      -0.254       0.372
C(countyfips)[T.51013]          -0.0626      0.160     -0.392      0.695      -0.376       0.251
C(countyfips)[T.51015]           0.0252      0.160      0.158      0.875      -0.288       0.338
C(countyfips)[T.51019]          -0.0118      0.160     -0.074      0.941      -0.325       0.302
C(countyfips)[T.51041]           0.0910      0.160      0.569      0.569      -0.222       0.404
C(countyfips)[T.51047]           0.1016      0.160      0.636      0.525      -0.212       0.415
C(countyfips)[T.51059]          -0.0670      0.160     -0.419      0.675      -0.380       0.246
C(countyfips)[T.51061]           0.0163      0.160      0.102      0.919      -0.297       0.330
C(countyfips)[T.51069]           0.1188      0.160      0.743      0.457      -0.194       0.432
C(countyfips)[T.51085]           0.0896      0.160      0.561      0.575      -0.224       0.403
C(countyfips)[T.51087]           0.0362      0.160      0.226      0.821      -0.277       0.349
C(countyfips)[T.51095]           0.0690      0.160      0.432      0.666      -0.244       0.382
C(countyfips)[T.51107]           0.0101      0.160      0.064      0.949      -0.303       0.323
C(countyfips)[T.51121]           0.0068      0.160      0.042      0.966      -0.307       0.320
C(countyfips)[T.51153]          -0.0229      0.160     -0.143      0.886      -0.336       0.290
C(countyfips)[T.51161]          -0.0269      0.160     -0.168      0.867      -0.340       0.286
C(countyfips)[T.51177]           0.0798      0.160      0.499      0.618      -0.234       0.393
C(countyfips)[T.51179]           0.0030      0.160      0.019      0.985      -0.310       0.316
C(countyfips)[T.51199]           0.0365      0.160      0.229      0.819      -0.277       0.350
C(countyfips)[T.51510]          -0.0368      0.160     -0.231      0.818      -0.350       0.276
C(countyfips)[T.51550]           0.0030      0.160      0.018      0.985      -0.310       0.316
C(countyfips)[T.51630]           0.0041      0.160      0.026      0.979      -0.309       0.317
C(countyfips)[T.51650]           0.0022      0.160      0.014      0.989      -0.311       0.315
C(countyfips)[T.51683]           0.0482      0.160      0.302      0.763      -0.265       0.361
C(countyfips)[T.51700]          -0.0260      0.160     -0.163      0.871      -0.339       0.287
C(countyfips)[T.51710]          -0.0014      0.160     -0.009      0.993      -0.315       0.312
C(countyfips)[T.51740]          -0.0475      0.160     -0.297      0.766      -0.361       0.266
C(countyfips)[T.51800]           0.0178      0.160      0.111      0.911      -0.296       0.331
C(countyfips)[T.51810]          -0.0282      0.160     -0.177      0.860      -0.341       0.285
C(countyfips)[T.51840]          -0.0210      0.160     -0.131      0.896      -0.334       0.292
C(countyfips)[T.53005]           0.0742      0.160      0.464      0.642      -0.239       0.388
C(countyfips)[T.53007]           0.0488      0.160      0.305      0.760      -0.264       0.362
C(countyfips)[T.53015]           0.0374      0.160      0.234      0.815      -0.276       0.351
C(countyfips)[T.53025]           0.0308      0.160      0.193      0.847      -0.282       0.344
C(countyfips)[T.53033]          -0.0778      0.160     -0.487      0.626      -0.391       0.235
C(countyfips)[T.53035]           0.1407      0.160      0.881      0.379      -0.173       0.454
C(countyfips)[T.53041]           0.0576      0.160      0.361      0.718      -0.256       0.371
C(countyfips)[T.53053]          -0.0020      0.160     -0.013      0.990      -0.315       0.311
C(countyfips)[T.53057]           0.0563      0.160      0.352      0.725      -0.257       0.369
C(countyfips)[T.53061]           0.0351      0.160      0.220      0.826      -0.278       0.348
C(countyfips)[T.53063]           0.0724      0.160      0.453      0.650      -0.241       0.386
C(countyfips)[T.53067]           0.0070      0.160      0.044      0.965      -0.306       0.320
C(countyfips)[T.53073]           0.0319      0.160      0.200      0.842      -0.281       0.345
C(countyfips)[T.54003]           0.0400      0.160      0.251      0.802      -0.273       0.353
C(countyfips)[T.54011]          -0.0201      0.160     -0.126      0.900      -0.333       0.293
C(countyfips)[T.54039]           0.0265      0.160      0.166      0.869      -0.287       0.340
C(countyfips)[T.54061]           0.0494      0.160      0.309      0.758      -0.264       0.363
C(countyfips)[T.55009]           0.0479      0.160      0.300      0.764      -0.265       0.361
C(countyfips)[T.55021]           0.0350      0.160      0.219      0.827      -0.278       0.348
C(countyfips)[T.55025]           0.0159      0.160      0.099      0.921      -0.297       0.329
C(countyfips)[T.55031]           0.0403      0.160      0.252      0.801      -0.273       0.354
C(countyfips)[T.55035]           0.0906      0.160      0.567      0.571      -0.223       0.404
C(countyfips)[T.55039]           0.0436      0.160      0.273      0.785      -0.270       0.357
C(countyfips)[T.55059]           0.0218      0.160      0.136      0.892      -0.291       0.335
C(countyfips)[T.55063]           0.0218      0.160      0.136      0.892      -0.292       0.335
C(countyfips)[T.55073]           0.0342      0.160      0.214      0.830      -0.279       0.347
C(countyfips)[T.55079]          -0.0263      0.160     -0.164      0.869      -0.340       0.287
C(countyfips)[T.55087]           0.0892      0.160      0.558      0.577      -0.224       0.402
C(countyfips)[T.55089]           0.0441      0.160      0.276      0.783      -0.269       0.357
C(countyfips)[T.55095]           0.0290      0.160      0.181      0.856      -0.284       0.342
C(countyfips)[T.55097]           0.0839      0.160      0.525      0.600      -0.229       0.397
C(countyfips)[T.55101]           0.0179      0.160      0.112      0.911      -0.295       0.331
C(countyfips)[T.55111]           0.0287      0.160      0.180      0.857      -0.285       0.342
C(countyfips)[T.55117]           0.0223      0.160      0.139      0.889      -0.291       0.336
C(countyfips)[T.55127]           0.0198      0.160      0.124      0.901      -0.294       0.333
C(countyfips)[T.55131]           0.0395      0.160      0.247      0.805      -0.274       0.353
C(countyfips)[T.55133]           0.0288      0.160      0.180      0.857      -0.284       0.342
C(countyfips)[T.55139]           0.0252      0.160      0.158      0.874      -0.288       0.339
C(countyfips)[T.56021]           0.0263      0.160      0.165      0.869      -0.287       0.340
C(countyfips)[T.56025]          -0.0302      0.160     -0.189      0.850      -0.343       0.283
l1_spend_all                    -0.0797      0.006    -13.986      0.000      -0.091      -0.069
l1_gps_retail_and_recreation    -0.0242      0.006     -4.037      0.000      -0.036      -0.012
l1_emp                           0.0189      0.006      3.164      0.002       0.007       0.031
l1_revenue_all                   0.0168      0.005      3.382      0.001       0.007       0.026
==============================================================================
Omnibus:                      497.377   Durbin-Watson:                   1.904
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1573.219
Skew:                          -0.052   Prob(JB):                         0.00
Kurtosis:                       4.741   Cond. No.                     1.08e+03
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.08e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

The model using the raw economic variables has a very poor fit. Looking at the economics variables, they are all significant at the 1% level, which is encouraging, but the model in general has a low F-stat and Adjusted R-squared.

Earlier, I described the potential benefit of using the residuals instead of the raw values of the economic variable. I test that theory by replacing the lagged economic variables with their lagged residuals and re-running the regression:

In [67]:
# Model with county fixed effects, using residuals
formula_fe_resid = 'net_flow_std ~  l1_spend_all_resid + l1_gps_retail_and_recreation_resid + l1_emp_resid + l1_revenue_all_resid + C(countyfips)'

model_num = model_num + 1
ols_model_resid = smf.ols(formula_fe_resid, data=long_data_train).fit()
model_stats = add_model_stats(long_data_test, ols_model_resid, model_num)
print(ols_model_resid.summary())
                            OLS Regression Results                            
==============================================================================
Dep. Variable:           net_flow_std   R-squared:                       0.041
Model:                            OLS   Adj. R-squared:                 -0.047
Method:                 Least Squares   F-statistic:                    0.4667
Date:                Sat, 17 Dec 2022   Prob (F-statistic):               1.00
Time:                        20:05:42   Log-Likelihood:                -5011.8
No. Observations:                7836   AIC:                         1.134e+04
Df Residuals:                    7179   BIC:                         1.591e+04
Df Model:                         656                                         
Covariance Type:            nonrobust                                         
======================================================================================================
                                         coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------------
Intercept                              0.0077      0.139      0.055      0.956      -0.265       0.281
C(countyfips)[T.1055]                 -0.2213      0.197     -1.125      0.261      -0.607       0.164
C(countyfips)[T.1069]                  0.0157      0.198      0.079      0.937      -0.373       0.404
C(countyfips)[T.1073]                 -0.1745      0.197     -0.887      0.375      -0.560       0.211
C(countyfips)[T.1081]                  0.0179      0.196      0.091      0.927      -0.367       0.402
C(countyfips)[T.1089]                 -0.1780      0.197     -0.902      0.367      -0.565       0.209
C(countyfips)[T.1095]                  0.1124      0.196      0.573      0.566      -0.272       0.497
C(countyfips)[T.1097]                 -0.1730      0.196     -0.883      0.377      -0.557       0.211
C(countyfips)[T.1101]                 -0.0859      0.196     -0.438      0.661      -0.470       0.298
C(countyfips)[T.1115]                 -0.0319      0.197     -0.162      0.871      -0.417       0.353
C(countyfips)[T.1117]                  0.1025      0.196      0.522      0.602      -0.282       0.487
C(countyfips)[T.1125]                  0.0898      0.196      0.458      0.647      -0.294       0.474
C(countyfips)[T.2020]                 -0.0810      0.199     -0.407      0.684      -0.472       0.310
C(countyfips)[T.2090]                 -0.1067      0.196     -0.544      0.587      -0.492       0.278
C(countyfips)[T.4005]                 -0.0444      0.197     -0.225      0.822      -0.431       0.342
C(countyfips)[T.4013]                 -0.0454      0.196     -0.231      0.817      -0.430       0.340
C(countyfips)[T.4015]                 -0.0275      0.196     -0.140      0.888      -0.412       0.357
C(countyfips)[T.4017]                 -0.0647      0.197     -0.328      0.743      -0.451       0.322
C(countyfips)[T.4019]                 -0.0484      0.197     -0.246      0.805      -0.434       0.337
C(countyfips)[T.4021]                 -0.0659      0.197     -0.334      0.738      -0.452       0.321
C(countyfips)[T.4025]                 -0.0980      0.197     -0.499      0.618      -0.483       0.287
C(countyfips)[T.5031]                 -0.2350      0.199     -1.180      0.238      -0.626       0.156
C(countyfips)[T.5045]                  0.0214      0.200      0.107      0.914      -0.370       0.413
C(countyfips)[T.5051]                 -0.0443      0.197     -0.225      0.822      -0.430       0.341
C(countyfips)[T.5143]                 -0.0030      0.197     -0.015      0.988      -0.390       0.384
C(countyfips)[T.6001]                 -0.2503      0.196     -1.276      0.202      -0.635       0.134
C(countyfips)[T.6007]                 -0.0382      0.196     -0.195      0.845      -0.422       0.346
C(countyfips)[T.6013]                 -0.1353      0.196     -0.690      0.490      -0.520       0.249
C(countyfips)[T.6017]                 -0.1980      0.198     -0.999      0.318      -0.586       0.191
C(countyfips)[T.6019]                 -0.0925      0.196     -0.472      0.637      -0.477       0.292
C(countyfips)[T.6023]                  0.1513      0.197      0.770      0.441      -0.234       0.537
C(countyfips)[T.6029]                 -0.0658      0.196     -0.336      0.737      -0.450       0.319
C(countyfips)[T.6037]                 -0.1677      0.196     -0.855      0.393      -0.552       0.217
C(countyfips)[T.6039]                 -0.2141      0.197     -1.088      0.277      -0.600       0.172
C(countyfips)[T.6041]                 -0.2991      0.196     -1.524      0.128      -0.684       0.086
C(countyfips)[T.6045]                 -0.1529      0.197     -0.778      0.437      -0.538       0.232
C(countyfips)[T.6047]                 -0.0134      0.196     -0.068      0.946      -0.398       0.371
C(countyfips)[T.6053]                 -0.1719      0.197     -0.875      0.382      -0.557       0.213
C(countyfips)[T.6059]                 -0.1574      0.196     -0.802      0.422      -0.542       0.227
C(countyfips)[T.6061]                 -0.0327      0.196     -0.167      0.868      -0.417       0.352
C(countyfips)[T.6065]                 -0.0718      0.196     -0.366      0.714      -0.456       0.313
C(countyfips)[T.6067]                 -0.1931      0.197     -0.980      0.327      -0.579       0.193
C(countyfips)[T.6069]                  0.0046      0.197      0.023      0.982      -0.382       0.391
C(countyfips)[T.6071]                 -0.2060      0.196     -1.051      0.293      -0.590       0.178
C(countyfips)[T.6073]                 -0.2383      0.196     -1.215      0.224      -0.623       0.146
C(countyfips)[T.6075]                  0.0311      0.196      0.158      0.874      -0.354       0.416
C(countyfips)[T.6077]                 -0.1789      0.196     -0.913      0.362      -0.563       0.205
C(countyfips)[T.6081]                 -0.2699      0.196     -1.377      0.168      -0.654       0.114
C(countyfips)[T.6083]                 -0.0423      0.196     -0.216      0.829      -0.427       0.343
C(countyfips)[T.6085]                 -0.1538      0.196     -0.784      0.433      -0.538       0.231
C(countyfips)[T.6087]                  0.0379      0.197      0.193      0.847      -0.348       0.423
C(countyfips)[T.6089]                 -0.0023      0.198     -0.012      0.991      -0.390       0.385
C(countyfips)[T.6095]                 -0.1453      0.196     -0.741      0.459      -0.530       0.239
C(countyfips)[T.6099]                 -0.0490      0.196     -0.249      0.803      -0.434       0.336
C(countyfips)[T.6101]                 -0.0500      0.197     -0.254      0.799      -0.436       0.336
C(countyfips)[T.6107]                 -0.0443      0.196     -0.225      0.822      -0.429       0.341
C(countyfips)[T.6111]                 -0.1899      0.196     -0.969      0.333      -0.574       0.194
C(countyfips)[T.6113]                 -0.0775      0.196     -0.395      0.693      -0.463       0.308
C(countyfips)[T.8001]                  0.1919      0.197      0.976      0.329      -0.194       0.577
C(countyfips)[T.8005]                 -0.0225      0.197     -0.114      0.909      -0.408       0.363
C(countyfips)[T.8013]                 -0.0322      0.197     -0.164      0.870      -0.417       0.353
C(countyfips)[T.8014]                 -0.1229      0.197     -0.624      0.533      -0.509       0.263
C(countyfips)[T.8031]                  0.0122      0.196      0.062      0.951      -0.373       0.397
C(countyfips)[T.8035]                 -0.0312      0.196     -0.159      0.874      -0.416       0.353
C(countyfips)[T.8037]                 -0.0720      0.199     -0.362      0.717      -0.462       0.318
C(countyfips)[T.8041]                  0.0178      0.196      0.091      0.928      -0.366       0.402
C(countyfips)[T.8045]                  0.0105      0.196      0.054      0.957      -0.374       0.395
C(countyfips)[T.8059]                 -0.2516      0.197     -1.277      0.202      -0.638       0.135
C(countyfips)[T.8077]                 -0.0611      0.197     -0.311      0.756      -0.447       0.325
C(countyfips)[T.8101]                 -0.0643      0.197     -0.327      0.744      -0.450       0.321
C(countyfips)[T.8107]                  0.0198      0.196      0.101      0.919      -0.365       0.404
C(countyfips)[T.8117]                  0.0039      0.197      0.020      0.984      -0.382       0.390
C(countyfips)[T.8123]                  0.3072      0.196      1.567      0.117      -0.077       0.691
C(countyfips)[T.9001]                 -0.0865      0.196     -0.441      0.660      -0.471       0.298
C(countyfips)[T.9003]                 -0.0657      0.196     -0.334      0.738      -0.451       0.319
C(countyfips)[T.9005]                 -0.1184      0.198     -0.599      0.549      -0.506       0.269
C(countyfips)[T.9007]                 -0.0647      0.197     -0.329      0.742      -0.450       0.321
C(countyfips)[T.9009]                 -0.0359      0.196     -0.183      0.855      -0.421       0.349
C(countyfips)[T.9011]                 -0.0837      0.198     -0.424      0.672      -0.471       0.303
C(countyfips)[T.9013]                  0.0174      0.197      0.089      0.929      -0.368       0.403
C(countyfips)[T.10001]                 0.0155      0.197      0.078      0.937      -0.371       0.402
C(countyfips)[T.10003]                -0.0083      0.196     -0.043      0.966      -0.393       0.376
C(countyfips)[T.12001]                -0.0323      0.196     -0.165      0.869      -0.417       0.352
C(countyfips)[T.12009]                -0.0548      0.196     -0.279      0.780      -0.440       0.330
C(countyfips)[T.12011]                -0.0441      0.196     -0.224      0.822      -0.429       0.341
C(countyfips)[T.12015]                -0.0792      0.197     -0.402      0.688      -0.466       0.307
C(countyfips)[T.12017]                -0.0633      0.197     -0.322      0.748      -0.449       0.322
C(countyfips)[T.12019]                -0.1574      0.198     -0.794      0.427      -0.546       0.231
C(countyfips)[T.12021]                -0.0410      0.196     -0.209      0.834      -0.425       0.343
C(countyfips)[T.12023]                -0.0804      0.197     -0.409      0.682      -0.466       0.305
C(countyfips)[T.12031]                 0.0428      0.197      0.218      0.828      -0.343       0.428
C(countyfips)[T.12033]                -0.2858      0.196     -1.459      0.144      -0.670       0.098
C(countyfips)[T.12035]                -0.0191      0.196     -0.098      0.922      -0.403       0.365
C(countyfips)[T.12053]                -0.0532      0.197     -0.270      0.787      -0.440       0.333
C(countyfips)[T.12055]                -0.0251      0.196     -0.128      0.898      -0.409       0.359
C(countyfips)[T.12057]                 0.0284      0.196      0.145      0.885      -0.356       0.413
C(countyfips)[T.12061]                -0.0434      0.197     -0.220      0.826      -0.429       0.343
C(countyfips)[T.12069]                -0.0273      0.196     -0.139      0.889      -0.412       0.357
C(countyfips)[T.12071]                -0.0640      0.196     -0.326      0.745      -0.449       0.321
C(countyfips)[T.12073]                -0.0287      0.196     -0.146      0.884      -0.413       0.356
C(countyfips)[T.12081]                -0.0508      0.196     -0.259      0.796      -0.436       0.334
C(countyfips)[T.12083]                -0.0556      0.196     -0.283      0.777      -0.440       0.329
C(countyfips)[T.12085]                -0.0607      0.196     -0.309      0.757      -0.446       0.324
C(countyfips)[T.12086]                -0.0542      0.196     -0.277      0.782      -0.439       0.330
C(countyfips)[T.12087]                -0.0637      0.197     -0.324      0.746      -0.449       0.322
C(countyfips)[T.12091]                -0.1077      0.198     -0.544      0.586      -0.496       0.280
C(countyfips)[T.12095]                -0.0650      0.196     -0.331      0.741      -0.450       0.320
C(countyfips)[T.12097]                 0.0118      0.196      0.060      0.952      -0.373       0.397
C(countyfips)[T.12099]                -0.0574      0.196     -0.293      0.770      -0.442       0.327
C(countyfips)[T.12101]                -0.0415      0.196     -0.212      0.832      -0.426       0.343
C(countyfips)[T.12103]                -0.0552      0.196     -0.281      0.779      -0.440       0.330
C(countyfips)[T.12105]                -0.0515      0.197     -0.262      0.794      -0.437       0.334
C(countyfips)[T.12107]                 0.0040      0.196      0.020      0.984      -0.381       0.389
C(countyfips)[T.12109]                -0.1041      0.197     -0.529      0.597      -0.490       0.282
C(countyfips)[T.12111]                -0.0526      0.196     -0.268      0.788      -0.437       0.332
C(countyfips)[T.12113]                -0.1734      0.200     -0.867      0.386      -0.565       0.219
C(countyfips)[T.12115]                -0.0439      0.196     -0.224      0.823      -0.428       0.340
C(countyfips)[T.12117]                 0.0556      0.196      0.283      0.777      -0.329       0.440
C(countyfips)[T.12119]                -0.0086      0.196     -0.044      0.965      -0.392       0.375
C(countyfips)[T.12127]                -0.0389      0.196     -0.199      0.843      -0.423       0.345
C(countyfips)[T.12131]                -0.0979      0.197     -0.496      0.620      -0.485       0.289
C(countyfips)[T.13013]                -0.2138      0.197     -1.086      0.278      -0.600       0.172
C(countyfips)[T.13015]                -0.0122      0.196     -0.062      0.950      -0.397       0.373
C(countyfips)[T.13021]                 0.0200      0.196      0.102      0.919      -0.364       0.404
C(countyfips)[T.13031]                -0.0689      0.198     -0.348      0.728      -0.457       0.319
C(countyfips)[T.13039]                -0.0539      0.198     -0.272      0.785      -0.442       0.334
C(countyfips)[T.13045]                -0.0632      0.196     -0.322      0.747      -0.447       0.321
C(countyfips)[T.13051]                 0.0091      0.197      0.046      0.963      -0.376       0.394
C(countyfips)[T.13057]                 0.0084      0.197      0.043      0.966      -0.377       0.394
C(countyfips)[T.13059]                -0.0238      0.197     -0.121      0.904      -0.409       0.362
C(countyfips)[T.13063]                -0.0945      0.197     -0.480      0.631      -0.481       0.292
C(countyfips)[T.13067]                 0.1369      0.196      0.698      0.485      -0.248       0.521
C(countyfips)[T.13073]                -0.2610      0.197     -1.326      0.185      -0.647       0.125
C(countyfips)[T.13077]                -0.0115      0.196     -0.059      0.953      -0.396       0.373
C(countyfips)[T.13089]                 0.0764      0.196      0.389      0.697      -0.309       0.462
C(countyfips)[T.13095]                -0.2007      0.198     -1.011      0.312      -0.590       0.188
C(countyfips)[T.13097]                -0.1760      0.196     -0.896      0.370      -0.561       0.209
C(countyfips)[T.13113]                -0.1834      0.197     -0.932      0.351      -0.569       0.202
C(countyfips)[T.13117]                 0.0606      0.196      0.309      0.758      -0.324       0.445
C(countyfips)[T.13121]                 0.0062      0.196      0.032      0.975      -0.378       0.391
C(countyfips)[T.13129]                -0.1602      0.196     -0.816      0.414      -0.545       0.224
C(countyfips)[T.13135]                -0.0667      0.196     -0.340      0.734      -0.451       0.318
C(countyfips)[T.13139]                 0.1003      0.197      0.510      0.610      -0.285       0.486
C(countyfips)[T.13151]                -0.0741      0.197     -0.377      0.707      -0.460       0.311
C(countyfips)[T.13153]                -0.1791      0.198     -0.903      0.367      -0.568       0.210
C(countyfips)[T.13179]                -0.1494      0.196     -0.760      0.447      -0.535       0.236
C(countyfips)[T.13185]                -0.0723      0.197     -0.368      0.713      -0.458       0.313
C(countyfips)[T.13215]                -0.0277      0.197     -0.141      0.888      -0.414       0.358
C(countyfips)[T.13217]                -0.0240      0.196     -0.122      0.903      -0.408       0.361
C(countyfips)[T.13245]                -0.1110      0.198     -0.562      0.574      -0.498       0.276
C(countyfips)[T.13247]                -0.0333      0.196     -0.170      0.865      -0.417       0.351
C(countyfips)[T.13275]                -0.0016      0.197     -0.008      0.993      -0.389       0.385
C(countyfips)[T.13297]                 0.0589      0.199      0.297      0.767      -0.330       0.448
C(countyfips)[T.13313]                -0.1243      0.197     -0.632      0.527      -0.510       0.261
C(countyfips)[T.15003]                -0.0356      0.196     -0.181      0.856      -0.421       0.349
C(countyfips)[T.16001]                 0.0295      0.196      0.150      0.881      -0.355       0.414
C(countyfips)[T.16005]                -0.1083      0.197     -0.549      0.583      -0.495       0.278
C(countyfips)[T.16017]                 0.0087      0.196      0.044      0.965      -0.376       0.393
C(countyfips)[T.16019]                -0.0428      0.196     -0.218      0.827      -0.427       0.341
C(countyfips)[T.16027]                 0.0529      0.196      0.270      0.787      -0.331       0.437
C(countyfips)[T.16055]                -0.1212      0.198     -0.613      0.540      -0.509       0.267
C(countyfips)[T.17031]                -0.1372      0.196     -0.699      0.485      -0.522       0.248
C(countyfips)[T.17037]                 0.0765      0.196      0.391      0.696      -0.307       0.460
C(countyfips)[T.17043]                -0.0262      0.196     -0.134      0.894      -0.410       0.358
C(countyfips)[T.17089]                -0.0471      0.196     -0.240      0.810      -0.431       0.337
C(countyfips)[T.17097]                -0.0044      0.196     -0.023      0.982      -0.389       0.380
C(countyfips)[T.17099]                 0.0138      0.196      0.071      0.944      -0.371       0.398
C(countyfips)[T.17111]                -0.0514      0.197     -0.262      0.794      -0.437       0.334
C(countyfips)[T.17119]                 0.1064      0.197      0.541      0.589      -0.279       0.492
C(countyfips)[T.17143]                -0.0228      0.196     -0.116      0.907      -0.406       0.361
C(countyfips)[T.17163]                -0.1604      0.196     -0.819      0.413      -0.544       0.223
C(countyfips)[T.17167]                 0.0448      0.196      0.228      0.819      -0.340       0.429
C(countyfips)[T.17183]                -0.0992      0.197     -0.503      0.615      -0.486       0.287
C(countyfips)[T.17197]                -0.0708      0.196     -0.361      0.718      -0.456       0.314
C(countyfips)[T.17201]                -0.0098      0.196     -0.050      0.960      -0.395       0.375
C(countyfips)[T.18003]                -0.0716      0.196     -0.365      0.715      -0.456       0.313
C(countyfips)[T.18011]                -0.0615      0.196     -0.313      0.754      -0.446       0.323
C(countyfips)[T.18057]                -0.0635      0.196     -0.324      0.746      -0.448       0.321
C(countyfips)[T.18063]                -0.0589      0.196     -0.300      0.764      -0.443       0.325
C(countyfips)[T.18081]                -0.1272      0.196     -0.648      0.517      -0.512       0.258
C(countyfips)[T.18091]                -0.0405      0.196     -0.206      0.837      -0.425       0.344
C(countyfips)[T.18097]                -0.1719      0.197     -0.874      0.382      -0.557       0.214
C(countyfips)[T.18127]                -0.0275      0.196     -0.140      0.889      -0.412       0.357
C(countyfips)[T.18163]                -0.1770      0.198     -0.893      0.372      -0.565       0.211
C(countyfips)[T.19013]                 0.0183      0.198      0.093      0.926      -0.370       0.406
C(countyfips)[T.19061]                -0.1409      0.197     -0.714      0.475      -0.528       0.246
C(countyfips)[T.19113]                -0.1552      0.196     -0.790      0.429      -0.540       0.230
C(countyfips)[T.19153]                 0.0809      0.196      0.413      0.680      -0.303       0.465
C(countyfips)[T.19155]                -0.1079      0.196     -0.549      0.583      -0.493       0.277
C(countyfips)[T.19163]                -0.0837      0.196     -0.427      0.670      -0.468       0.301
C(countyfips)[T.19169]                 0.0073      0.196      0.037      0.970      -0.377       0.391
C(countyfips)[T.19193]                 0.1023      0.196      0.522      0.601      -0.281       0.486
C(countyfips)[T.20045]                -0.0633      0.197     -0.321      0.748      -0.449       0.323
C(countyfips)[T.20173]                -0.0051      0.196     -0.026      0.979      -0.390       0.380
C(countyfips)[T.20209]                -0.3648      0.196     -1.859      0.063      -0.749       0.020
C(countyfips)[T.21015]                 0.0398      0.196      0.203      0.839      -0.344       0.424
C(countyfips)[T.21037]                -0.1247      0.197     -0.633      0.526      -0.511       0.261
C(countyfips)[T.21059]                -0.0339      0.197     -0.172      0.863      -0.420       0.352
C(countyfips)[T.21067]                -0.1160      0.196     -0.592      0.554      -0.500       0.268
C(countyfips)[T.21111]                -0.1359      0.196     -0.692      0.489      -0.521       0.249
C(countyfips)[T.21199]                -0.0584      0.198     -0.295      0.768      -0.447       0.330
C(countyfips)[T.21227]                 0.0055      0.196      0.028      0.978      -0.380       0.391
C(countyfips)[T.22005]                 0.1384      0.197      0.704      0.481      -0.247       0.524
C(countyfips)[T.22017]                -0.0295      0.196     -0.150      0.881      -0.415       0.356
C(countyfips)[T.22033]                -0.1246      0.197     -0.632      0.527      -0.511       0.262
C(countyfips)[T.22051]                 0.1824      0.197      0.925      0.355      -0.204       0.569
C(countyfips)[T.22055]                 0.0041      0.198      0.021      0.983      -0.384       0.392
C(countyfips)[T.22063]                 0.0754      0.197      0.383      0.702      -0.310       0.461
C(countyfips)[T.22071]                 0.0004      0.197      0.002      0.998      -0.386       0.387
C(countyfips)[T.22073]                -0.2417      0.198     -1.221      0.222      -0.630       0.146
C(countyfips)[T.22103]                 0.0620      0.197      0.314      0.753      -0.325       0.449
C(countyfips)[T.22105]                 0.2636      0.198      1.330      0.183      -0.125       0.652
C(countyfips)[T.22109]                 0.4110      0.198      2.072      0.038       0.022       0.800
C(countyfips)[T.23001]                 0.0413      0.197      0.210      0.834      -0.345       0.428
C(countyfips)[T.23005]                -0.0388      0.197     -0.197      0.844      -0.424       0.347
C(countyfips)[T.23019]                 0.0434      0.196      0.221      0.825      -0.341       0.427
C(countyfips)[T.24001]                 0.0264      0.197      0.134      0.893      -0.359       0.412
C(countyfips)[T.24003]                -0.0170      0.196     -0.087      0.931      -0.402       0.368
C(countyfips)[T.24005]                -0.0546      0.197     -0.278      0.781      -0.440       0.331
C(countyfips)[T.24009]                -0.0873      0.197     -0.444      0.657      -0.473       0.298
C(countyfips)[T.24013]                -0.1308      0.197     -0.665      0.506      -0.516       0.255
C(countyfips)[T.24017]                -0.1515      0.196     -0.772      0.440      -0.536       0.233
C(countyfips)[T.24021]                -0.0627      0.197     -0.319      0.750      -0.448       0.323
C(countyfips)[T.24025]                -0.0389      0.197     -0.198      0.843      -0.425       0.347
C(countyfips)[T.24027]                -0.0698      0.196     -0.356      0.722      -0.454       0.314
C(countyfips)[T.24031]                -0.2132      0.196     -1.087      0.277      -0.598       0.171
C(countyfips)[T.24033]                -0.3317      0.196     -1.689      0.091      -0.717       0.053
C(countyfips)[T.24043]                -0.0661      0.196     -0.337      0.736      -0.450       0.318
C(countyfips)[T.24510]                -0.1477      0.197     -0.750      0.453      -0.534       0.238
C(countyfips)[T.25001]                -0.0754      0.199     -0.379      0.705      -0.465       0.314
C(countyfips)[T.25003]                -0.0355      0.199     -0.179      0.858      -0.425       0.354
C(countyfips)[T.25017]                -0.0475      0.196     -0.242      0.809      -0.432       0.337
C(countyfips)[T.25021]                -0.0507      0.196     -0.258      0.796      -0.436       0.334
C(countyfips)[T.25023]                -0.0217      0.197     -0.110      0.912      -0.407       0.364
C(countyfips)[T.25025]                -0.0624      0.197     -0.317      0.752      -0.449       0.324
C(countyfips)[T.25027]                -0.0339      0.196     -0.173      0.863      -0.419       0.351
C(countyfips)[T.26045]                -0.0325      0.197     -0.165      0.869      -0.419       0.354
C(countyfips)[T.26049]                -0.0636      0.198     -0.322      0.748      -0.451       0.324
C(countyfips)[T.26065]                 0.0044      0.196      0.023      0.982      -0.380       0.389
C(countyfips)[T.26077]                -0.0974      0.199     -0.489      0.625      -0.488       0.293
C(countyfips)[T.26081]                -0.0202      0.197     -0.103      0.918      -0.405       0.365
C(countyfips)[T.26099]                -0.0769      0.197     -0.391      0.696      -0.463       0.309
C(countyfips)[T.26121]                -0.1297      0.200     -0.650      0.516      -0.521       0.261
C(countyfips)[T.26125]                -0.0759      0.197     -0.386      0.700      -0.462       0.310
C(countyfips)[T.26139]                -0.0789      0.197     -0.400      0.689      -0.466       0.308
C(countyfips)[T.26145]                -0.0598      0.197     -0.304      0.761      -0.446       0.326
C(countyfips)[T.26147]                -0.1033      0.198     -0.522      0.602      -0.491       0.285
C(countyfips)[T.26161]                -0.0253      0.196     -0.129      0.898      -0.410       0.360
C(countyfips)[T.26163]                -0.0851      0.197     -0.432      0.666      -0.472       0.301
C(countyfips)[T.27003]                -0.0087      0.196     -0.044      0.965      -0.393       0.375
C(countyfips)[T.27005]                -0.0622      0.198     -0.314      0.754      -0.451       0.326
C(countyfips)[T.27013]                -0.0283      0.197     -0.144      0.886      -0.414       0.357
C(countyfips)[T.27019]                -0.1286      0.196     -0.655      0.512      -0.513       0.256
C(countyfips)[T.27025]                -0.0609      0.197     -0.309      0.757      -0.447       0.325
C(countyfips)[T.27035]                -0.0186      0.197     -0.094      0.925      -0.404       0.367
C(countyfips)[T.27037]                -0.0307      0.196     -0.157      0.875      -0.415       0.354
C(countyfips)[T.27053]                -0.0570      0.196     -0.291      0.771      -0.442       0.327
C(countyfips)[T.27109]                 0.0120      0.196      0.061      0.951      -0.373       0.397
C(countyfips)[T.27123]                -0.0617      0.196     -0.315      0.753      -0.446       0.323
C(countyfips)[T.27131]                 0.0091      0.198      0.046      0.963      -0.378       0.396
C(countyfips)[T.27137]                -0.0148      0.196     -0.075      0.940      -0.400       0.370
C(countyfips)[T.27139]                 0.0596      0.196      0.303      0.762      -0.325       0.444
C(countyfips)[T.27145]                -0.0171      0.196     -0.087      0.930      -0.402       0.367
C(countyfips)[T.27163]                -0.0155      0.196     -0.079      0.937      -0.400       0.369
C(countyfips)[T.27171]                 0.0331      0.196      0.169      0.866      -0.351       0.417
C(countyfips)[T.28033]                 0.0233      0.197      0.118      0.906      -0.363       0.409
C(countyfips)[T.28047]                -0.1439      0.198     -0.729      0.466      -0.531       0.243
C(countyfips)[T.28049]                -0.1324      0.197     -0.672      0.502      -0.519       0.254
C(countyfips)[T.28059]                 0.0586      0.198      0.295      0.768      -0.330       0.447
C(countyfips)[T.28089]                 0.0229      0.196      0.117      0.907      -0.362       0.408
C(countyfips)[T.28121]                -0.3847      0.204     -1.881      0.060      -0.785       0.016
C(countyfips)[T.29019]                -0.0588      0.196     -0.300      0.764      -0.443       0.326
C(countyfips)[T.29021]                 0.0872      0.196      0.444      0.657      -0.298       0.472
C(countyfips)[T.29029]                -0.0561      0.197     -0.285      0.776      -0.443       0.330
C(countyfips)[T.29031]                -0.0036      0.197     -0.018      0.986      -0.389       0.382
C(countyfips)[T.29047]                -0.0281      0.196     -0.143      0.886      -0.413       0.357
C(countyfips)[T.29071]                -0.1327      0.197     -0.675      0.500      -0.518       0.253
C(countyfips)[T.29077]                -0.0217      0.196     -0.111      0.912      -0.406       0.363
C(countyfips)[T.29095]                -0.0320      0.196     -0.163      0.871      -0.416       0.352
C(countyfips)[T.29097]                -0.1209      0.197     -0.613      0.540      -0.508       0.266
C(countyfips)[T.29099]                -0.0829      0.196     -0.422      0.673      -0.468       0.302
C(countyfips)[T.29145]                 0.0052      0.200      0.026      0.979      -0.386       0.397
C(countyfips)[T.29183]                -0.0638      0.196     -0.325      0.745      -0.449       0.321
C(countyfips)[T.29189]                -0.1164      0.197     -0.591      0.554      -0.502       0.270
C(countyfips)[T.29510]                -0.1550      0.196     -0.790      0.429      -0.540       0.230
C(countyfips)[T.30029]                -0.0394      0.197     -0.200      0.842      -0.426       0.348
C(countyfips)[T.30049]                -0.0022      0.196     -0.011      0.991      -0.386       0.382
C(countyfips)[T.30063]                -0.1207      0.198     -0.610      0.542      -0.509       0.267
C(countyfips)[T.30111]                -0.0653      0.199     -0.329      0.743      -0.455       0.324
C(countyfips)[T.31019]                 0.0463      0.197      0.236      0.814      -0.339       0.432
C(countyfips)[T.31055]                -0.1108      0.196     -0.566      0.571      -0.495       0.273
C(countyfips)[T.31079]                -0.0227      0.196     -0.116      0.908      -0.407       0.362
C(countyfips)[T.31109]                -0.1855      0.197     -0.943      0.346      -0.571       0.200
C(countyfips)[T.31153]                 0.0010      0.196      0.005      0.996      -0.383       0.386
C(countyfips)[T.32003]                -0.0407      0.196     -0.207      0.836      -0.426       0.344
C(countyfips)[T.32005]                 0.0380      0.198      0.192      0.848      -0.350       0.426
C(countyfips)[T.32031]                 0.1033      0.196      0.526      0.599      -0.281       0.488
C(countyfips)[T.32510]                 0.1093      0.196      0.558      0.577      -0.275       0.493
C(countyfips)[T.33001]                -0.0228      0.196     -0.116      0.908      -0.408       0.362
C(countyfips)[T.33003]                -0.1098      0.200     -0.549      0.583      -0.502       0.282
C(countyfips)[T.33005]                -0.0653      0.197     -0.331      0.741      -0.452       0.321
C(countyfips)[T.33011]                -0.0124      0.197     -0.063      0.950      -0.399       0.374
C(countyfips)[T.33015]                -0.0455      0.197     -0.231      0.817      -0.432       0.341
C(countyfips)[T.33017]                -0.0637      0.196     -0.324      0.746      -0.449       0.322
C(countyfips)[T.34001]                -0.1079      0.200     -0.540      0.589      -0.499       0.284
C(countyfips)[T.34003]                -0.1814      0.196     -0.924      0.355      -0.566       0.203
C(countyfips)[T.34009]                -0.1538      0.202     -0.762      0.446      -0.550       0.242
C(countyfips)[T.34011]                -0.0924      0.198     -0.467      0.641      -0.481       0.296
C(countyfips)[T.34015]                -0.1297      0.198     -0.654      0.513      -0.519       0.259
C(countyfips)[T.34017]                -0.1505      0.196     -0.766      0.444      -0.536       0.235
C(countyfips)[T.34019]                -0.1149      0.197     -0.583      0.560      -0.501       0.272
C(countyfips)[T.34021]                -0.0854      0.196     -0.436      0.663      -0.470       0.299
C(countyfips)[T.34023]                -0.1532      0.196     -0.780      0.435      -0.538       0.232
C(countyfips)[T.34025]                -0.1048      0.197     -0.532      0.595      -0.491       0.281
C(countyfips)[T.34027]                -0.0874      0.197     -0.445      0.657      -0.473       0.298
C(countyfips)[T.34029]                -0.0844      0.198     -0.426      0.670      -0.473       0.304
C(countyfips)[T.34031]                -0.3443      0.197     -1.749      0.080      -0.730       0.042
C(countyfips)[T.34035]                -0.0488      0.197     -0.248      0.804      -0.435       0.337
C(countyfips)[T.34037]                -0.1655      0.198     -0.835      0.404      -0.554       0.223
C(countyfips)[T.34039]                -0.3752      0.197     -1.902      0.057      -0.762       0.011
C(countyfips)[T.35001]                -0.2100      0.197     -1.069      0.285      -0.595       0.175
C(countyfips)[T.35013]                -0.0319      0.197     -0.162      0.871      -0.418       0.354
C(countyfips)[T.35045]                -0.1197      0.198     -0.604      0.546      -0.508       0.269
C(countyfips)[T.35049]                -0.1352      0.196     -0.689      0.491      -0.520       0.250
C(countyfips)[T.35055]                -0.0298      0.196     -0.152      0.879      -0.414       0.354
C(countyfips)[T.36009]                -0.0051      0.198     -0.026      0.979      -0.392       0.382
C(countyfips)[T.36013]                -0.0281      0.197     -0.143      0.887      -0.415       0.358
C(countyfips)[T.36015]                 0.0252      0.196      0.129      0.898      -0.360       0.410
C(countyfips)[T.36019]                -0.0686      0.198     -0.346      0.729      -0.457       0.320
C(countyfips)[T.36027]                -0.0383      0.197     -0.194      0.846      -0.424       0.348
C(countyfips)[T.36029]                -0.0454      0.197     -0.231      0.817      -0.431       0.340
C(countyfips)[T.36035]                 0.0053      0.197      0.027      0.978      -0.381       0.392
C(countyfips)[T.36039]                -0.0985      0.201     -0.491      0.624      -0.492       0.295
C(countyfips)[T.36043]                -0.1056      0.198     -0.533      0.594      -0.494       0.283
C(countyfips)[T.36045]                -0.0783      0.199     -0.394      0.694      -0.468       0.311
C(countyfips)[T.36051]                -0.0481      0.196     -0.245      0.806      -0.433       0.336
C(countyfips)[T.36053]                -0.0473      0.198     -0.239      0.811      -0.435       0.340
C(countyfips)[T.36055]                -0.0486      0.196     -0.247      0.805      -0.434       0.337
C(countyfips)[T.36059]                -0.0926      0.197     -0.469      0.639      -0.479       0.294
C(countyfips)[T.36061]                 0.1060      0.196      0.540      0.589      -0.279       0.491
C(countyfips)[T.36063]                -0.0369      0.198     -0.187      0.852      -0.424       0.350
C(countyfips)[T.36065]                -0.0772      0.197     -0.392      0.695      -0.463       0.309
C(countyfips)[T.36067]                -0.0243      0.197     -0.123      0.902      -0.410       0.361
C(countyfips)[T.36069]                -0.0259      0.197     -0.132      0.895      -0.411       0.360
C(countyfips)[T.36071]                -0.0194      0.197     -0.098      0.922      -0.406       0.367
C(countyfips)[T.36075]                -0.0339      0.197     -0.172      0.863      -0.420       0.352
C(countyfips)[T.36077]                -0.0172      0.197     -0.087      0.930      -0.403       0.369
C(countyfips)[T.36079]                -0.1222      0.197     -0.620      0.536      -0.509       0.264
C(countyfips)[T.36081]                -0.0929      0.197     -0.472      0.637      -0.479       0.293
C(countyfips)[T.36085]                -0.1459      0.196     -0.743      0.457      -0.531       0.239
C(countyfips)[T.36087]                -0.0861      0.197     -0.437      0.662      -0.473       0.300
C(countyfips)[T.36089]                -0.0430      0.197     -0.218      0.827      -0.429       0.343
C(countyfips)[T.36091]                -0.0219      0.197     -0.111      0.912      -0.408       0.364
C(countyfips)[T.36093]                -0.0399      0.196     -0.203      0.839      -0.425       0.345
C(countyfips)[T.36101]                -0.0188      0.197     -0.095      0.924      -0.405       0.368
C(countyfips)[T.36103]                -0.0636      0.197     -0.323      0.747      -0.450       0.323
C(countyfips)[T.36105]                -0.0552      0.197     -0.281      0.779      -0.441       0.331
C(countyfips)[T.36111]                -0.0961      0.198     -0.486      0.627      -0.483       0.291
C(countyfips)[T.36113]                -0.1116      0.200     -0.559      0.576      -0.503       0.280
C(countyfips)[T.36119]                -0.1338      0.196     -0.681      0.496      -0.519       0.251
C(countyfips)[T.37001]                -0.0420      0.196     -0.214      0.830      -0.427       0.343
C(countyfips)[T.37019]                -0.1093      0.199     -0.549      0.583      -0.500       0.281
C(countyfips)[T.37021]                 0.0375      0.196      0.191      0.849      -0.347       0.423
C(countyfips)[T.37025]                 0.0295      0.196      0.151      0.880      -0.355       0.414
C(countyfips)[T.37027]                 0.1227      0.196      0.625      0.532      -0.262       0.507
C(countyfips)[T.37031]                -0.0740      0.197     -0.375      0.708      -0.461       0.313
C(countyfips)[T.37035]                 0.0904      0.197      0.460      0.646      -0.295       0.476
C(countyfips)[T.37037]                -0.0354      0.197     -0.180      0.857      -0.421       0.350
C(countyfips)[T.37045]                -0.1049      0.197     -0.531      0.595      -0.492       0.282
C(countyfips)[T.37047]                -0.1667      0.196     -0.849      0.396      -0.551       0.218
C(countyfips)[T.37049]                -0.1881      0.196     -0.959      0.338      -0.573       0.197
C(countyfips)[T.37051]                -0.2642      0.197     -1.343      0.179      -0.650       0.122
C(countyfips)[T.37055]                -0.2080      0.202     -1.027      0.304      -0.605       0.189
C(countyfips)[T.37057]                -0.0990      0.196     -0.505      0.614      -0.483       0.285
C(countyfips)[T.37059]                -0.0117      0.196     -0.060      0.952      -0.396       0.373
C(countyfips)[T.37063]                -0.0288      0.196     -0.146      0.884      -0.414       0.356
C(countyfips)[T.37067]                 0.0556      0.196      0.283      0.777      -0.329       0.441
C(countyfips)[T.37071]                -0.0928      0.196     -0.474      0.636      -0.477       0.291
C(countyfips)[T.37081]                -0.3250      0.196     -1.659      0.097      -0.709       0.059
C(countyfips)[T.37085]                -0.1057      0.197     -0.537      0.591      -0.491       0.280
C(countyfips)[T.37087]                 0.0203      0.197      0.103      0.918      -0.366       0.406
C(countyfips)[T.37089]                -0.0590      0.197     -0.300      0.764      -0.445       0.327
C(countyfips)[T.37097]                -0.0256      0.197     -0.130      0.897      -0.412       0.361
C(countyfips)[T.37101]                 0.0105      0.197      0.053      0.958      -0.376       0.397
C(countyfips)[T.37105]                 0.1167      0.196      0.594      0.553      -0.268       0.502
C(countyfips)[T.37109]                 0.0437      0.196      0.223      0.824      -0.341       0.428
C(countyfips)[T.37119]                 0.0597      0.197      0.304      0.761      -0.326       0.445
C(countyfips)[T.37125]                -0.1040      0.197     -0.529      0.597      -0.490       0.282
C(countyfips)[T.37127]                -0.3676      0.196     -1.873      0.061      -0.752       0.017
C(countyfips)[T.37129]                -0.0816      0.196     -0.416      0.678      -0.467       0.303
C(countyfips)[T.37133]                -0.1537      0.198     -0.778      0.437      -0.541       0.234
C(countyfips)[T.37135]                -0.0901      0.197     -0.456      0.648      -0.477       0.297
C(countyfips)[T.37139]                -0.2456      0.197     -1.249      0.212      -0.631       0.140
C(countyfips)[T.37147]                -0.0802      0.196     -0.408      0.683      -0.465       0.305
C(countyfips)[T.37151]                -0.1807      0.196     -0.920      0.357      -0.566       0.204
C(countyfips)[T.37155]                -0.0181      0.199     -0.091      0.927      -0.409       0.372
C(countyfips)[T.37157]                -0.1446      0.197     -0.736      0.462      -0.530       0.241
C(countyfips)[T.37159]                 0.0262      0.196      0.133      0.894      -0.358       0.411
C(countyfips)[T.37161]                 0.0368      0.199      0.185      0.853      -0.354       0.427
C(countyfips)[T.37163]                -0.0198      0.197     -0.101      0.920      -0.406       0.366
C(countyfips)[T.37167]                 0.0898      0.196      0.457      0.647      -0.295       0.475
C(countyfips)[T.37169]                -0.0130      0.196     -0.066      0.947      -0.397       0.371
C(countyfips)[T.37179]                -0.2112      0.197     -1.074      0.283      -0.597       0.174
C(countyfips)[T.37183]                 0.1421      0.196      0.723      0.470      -0.243       0.527
C(countyfips)[T.37189]                -0.0126      0.197     -0.064      0.949      -0.400       0.374
C(countyfips)[T.37191]                -0.0500      0.197     -0.254      0.799      -0.436       0.336
C(countyfips)[T.37193]                 0.0205      0.196      0.105      0.917      -0.364       0.405
C(countyfips)[T.37195]                -0.3251      0.197     -1.650      0.099      -0.711       0.061
C(countyfips)[T.38017]                -0.1046      0.197     -0.531      0.595      -0.490       0.281
C(countyfips)[T.38035]                -0.1159      0.196     -0.590      0.555      -0.501       0.269
C(countyfips)[T.39017]                -0.0230      0.196     -0.118      0.906      -0.407       0.361
C(countyfips)[T.39025]                 0.0393      0.196      0.200      0.841      -0.345       0.424
C(countyfips)[T.39035]                -0.0737      0.197     -0.375      0.708      -0.459       0.312
C(countyfips)[T.39041]                -0.0127      0.196     -0.065      0.949      -0.398       0.372
C(countyfips)[T.39043]                -0.0207      0.196     -0.106      0.916      -0.405       0.364
C(countyfips)[T.39045]                -0.0739      0.196     -0.377      0.706      -0.459       0.311
C(countyfips)[T.39049]                -0.0156      0.196     -0.080      0.937      -0.400       0.369
C(countyfips)[T.39055]                 0.0010      0.196      0.005      0.996      -0.383       0.385
C(countyfips)[T.39057]                -0.0470      0.197     -0.239      0.811      -0.433       0.339
C(countyfips)[T.39061]                -0.1274      0.196     -0.650      0.516      -0.512       0.257
C(countyfips)[T.39085]                -0.0611      0.197     -0.310      0.757      -0.447       0.325
C(countyfips)[T.39089]                -0.0026      0.196     -0.013      0.990      -0.387       0.382
C(countyfips)[T.39093]                -0.0667      0.197     -0.338      0.735      -0.453       0.320
C(countyfips)[T.39095]                -0.0992      0.196     -0.505      0.613      -0.484       0.286
C(countyfips)[T.39099]                -0.0148      0.197     -0.075      0.940      -0.401       0.371
C(countyfips)[T.39103]                -0.0422      0.196     -0.215      0.830      -0.427       0.342
C(countyfips)[T.39109]                -0.0479      0.197     -0.244      0.807      -0.434       0.338
C(countyfips)[T.39113]                -0.0662      0.197     -0.337      0.736      -0.452       0.319
C(countyfips)[T.39119]                -0.0122      0.196     -0.062      0.950      -0.397       0.372
C(countyfips)[T.39123]                -0.0098      0.198     -0.049      0.961      -0.399       0.379
C(countyfips)[T.39133]                 0.0681      0.196      0.347      0.728      -0.316       0.453
C(countyfips)[T.39147]                -0.0795      0.198     -0.402      0.688      -0.467       0.308
C(countyfips)[T.39151]                 0.0450      0.197      0.228      0.820      -0.342       0.432
C(countyfips)[T.39153]                -0.0679      0.198     -0.343      0.731      -0.455       0.320
C(countyfips)[T.39155]                 0.0226      0.197      0.115      0.909      -0.364       0.409
C(countyfips)[T.39157]                 0.0359      0.196      0.183      0.855      -0.349       0.421
C(countyfips)[T.39165]                -0.0201      0.196     -0.102      0.919      -0.405       0.365
C(countyfips)[T.39169]                -0.1126      0.198     -0.570      0.569      -0.500       0.275
C(countyfips)[T.40031]              3.528e-05      0.197      0.000      1.000      -0.385       0.385
C(countyfips)[T.40119]                 0.0302      0.197      0.154      0.878      -0.355       0.416
C(countyfips)[T.40143]                -0.1722      0.196     -0.877      0.380      -0.557       0.213
C(countyfips)[T.41005]                -0.0958      0.196     -0.488      0.626      -0.481       0.289
C(countyfips)[T.41007]                -0.0516      0.198     -0.260      0.795      -0.441       0.337
C(countyfips)[T.41011]                -0.0354      0.198     -0.179      0.858      -0.423       0.352
C(countyfips)[T.41017]                 0.0064      0.197      0.032      0.974      -0.380       0.392
C(countyfips)[T.41019]                 0.0112      0.196      0.057      0.955      -0.374       0.396
C(countyfips)[T.41029]                -0.3457      0.196     -1.763      0.078      -0.730       0.039
C(countyfips)[T.41033]                -0.0874      0.197     -0.443      0.658      -0.474       0.300
C(countyfips)[T.41035]                -0.0819      0.197     -0.415      0.678      -0.469       0.305
C(countyfips)[T.41039]                -0.1284      0.197     -0.653      0.514      -0.514       0.257
C(countyfips)[T.41041]                -0.1737      0.198     -0.879      0.379      -0.561       0.214
C(countyfips)[T.41043]                -0.0085      0.197     -0.043      0.965      -0.395       0.378
C(countyfips)[T.41047]                 0.0719      0.196      0.366      0.714      -0.313       0.457
C(countyfips)[T.41051]                -0.0546      0.197     -0.278      0.781      -0.440       0.331
C(countyfips)[T.41059]                -0.2287      0.199     -1.151      0.250      -0.618       0.161
C(countyfips)[T.41067]                 0.0521      0.196      0.266      0.790      -0.333       0.437
C(countyfips)[T.42003]                -0.0890      0.196     -0.453      0.650      -0.474       0.296
C(countyfips)[T.42007]                 0.0821      0.196      0.418      0.676      -0.303       0.467
C(countyfips)[T.42011]                -0.1923      0.196     -0.979      0.327      -0.577       0.193
C(countyfips)[T.42013]                 0.0495      0.196      0.253      0.800      -0.334       0.433
C(countyfips)[T.42015]                -0.0531      0.197     -0.269      0.788      -0.439       0.333
C(countyfips)[T.42017]                -0.0504      0.196     -0.257      0.797      -0.435       0.334
C(countyfips)[T.42019]                 0.0133      0.196      0.068      0.946      -0.371       0.398
C(countyfips)[T.42021]                -0.0097      0.196     -0.049      0.961      -0.395       0.375
C(countyfips)[T.42027]                -0.0262      0.196     -0.134      0.894      -0.411       0.358
C(countyfips)[T.42029]                 0.0802      0.196      0.408      0.683      -0.305       0.465
C(countyfips)[T.42033]                -0.0123      0.197     -0.062      0.950      -0.398       0.374
C(countyfips)[T.42041]                -0.0173      0.197     -0.088      0.930      -0.403       0.368
C(countyfips)[T.42043]                -0.0454      0.196     -0.232      0.817      -0.430       0.339
C(countyfips)[T.42045]                -0.1045      0.197     -0.531      0.595      -0.490       0.281
C(countyfips)[T.42049]                -0.0151      0.196     -0.077      0.939      -0.400       0.370
C(countyfips)[T.42051]                 0.0017      0.197      0.009      0.993      -0.384       0.388
C(countyfips)[T.42055]                 0.0207      0.197      0.105      0.916      -0.365       0.406
C(countyfips)[T.42063]                 0.0829      0.196      0.423      0.672      -0.302       0.467
C(countyfips)[T.42065]                 0.0540      0.197      0.274      0.784      -0.333       0.441
C(countyfips)[T.42069]                -0.1397      0.197     -0.710      0.478      -0.526       0.246
C(countyfips)[T.42071]                -0.0741      0.196     -0.378      0.706      -0.459       0.311
C(countyfips)[T.42073]                -0.0362      0.197     -0.184      0.854      -0.422       0.349
C(countyfips)[T.42075]                -0.1354      0.197     -0.689      0.491      -0.521       0.250
C(countyfips)[T.42077]                -0.0704      0.196     -0.359      0.720      -0.455       0.314
C(countyfips)[T.42079]                -0.2380      0.197     -1.210      0.226      -0.624       0.147
C(countyfips)[T.42085]                -0.0836      0.197     -0.424      0.672      -0.470       0.303
C(countyfips)[T.42089]                -0.1575      0.198     -0.794      0.427      -0.546       0.231
C(countyfips)[T.42091]                -0.0887      0.197     -0.450      0.652      -0.475       0.297
C(countyfips)[T.42095]                -0.0606      0.197     -0.308      0.758      -0.446       0.325
C(countyfips)[T.42097]                 0.1003      0.196      0.511      0.609      -0.285       0.485
C(countyfips)[T.42103]                -0.1176      0.200     -0.587      0.557      -0.510       0.275
C(countyfips)[T.42115]                 0.0453      0.197      0.230      0.818      -0.340       0.431
C(countyfips)[T.42125]                 0.0742      0.196      0.379      0.705      -0.310       0.458
C(countyfips)[T.42129]                -0.0007      0.196     -0.004      0.997      -0.385       0.384
C(countyfips)[T.42133]                 0.0412      0.196      0.210      0.834      -0.344       0.426
C(countyfips)[T.44003]                -0.0216      0.198     -0.109      0.913      -0.409       0.366
C(countyfips)[T.44007]                -0.1082      0.197     -0.550      0.583      -0.494       0.278
C(countyfips)[T.44009]                -0.0450      0.197     -0.228      0.820      -0.432       0.342
C(countyfips)[T.45003]                -0.1725      0.199     -0.868      0.386      -0.562       0.217
C(countyfips)[T.45007]                 0.0942      0.196      0.479      0.632      -0.291       0.479
C(countyfips)[T.45015]                 0.0657      0.197      0.333      0.739      -0.321       0.452
C(countyfips)[T.45019]                -0.1245      0.197     -0.631      0.528      -0.511       0.262
C(countyfips)[T.45035]                -0.0995      0.197     -0.505      0.613      -0.486       0.287
C(countyfips)[T.45043]                -0.0713      0.200     -0.357      0.721      -0.463       0.320
C(countyfips)[T.45045]                 0.0739      0.196      0.376      0.707      -0.311       0.459
C(countyfips)[T.45051]                -0.1508      0.205     -0.736      0.462      -0.552       0.251
C(countyfips)[T.45057]                 0.1572      0.197      0.799      0.424      -0.229       0.543
C(countyfips)[T.45063]                -0.0855      0.196     -0.435      0.663      -0.471       0.300
C(countyfips)[T.45077]                -0.1745      0.197     -0.886      0.376      -0.561       0.212
C(countyfips)[T.45079]                 0.0987      0.197      0.501      0.616      -0.287       0.485
C(countyfips)[T.45083]                -0.1682      0.197     -0.855      0.393      -0.554       0.218
C(countyfips)[T.45085]                -0.0910      0.197     -0.461      0.645      -0.478       0.296
C(countyfips)[T.45091]                -0.1716      0.197     -0.873      0.383      -0.557       0.214
C(countyfips)[T.46099]                -0.0640      0.196     -0.327      0.744      -0.448       0.320
C(countyfips)[T.46103]                -0.0915      0.198     -0.461      0.645      -0.480       0.297
C(countyfips)[T.47001]                 0.0722      0.197      0.367      0.714      -0.314       0.458
C(countyfips)[T.47009]                 0.0252      0.196      0.128      0.898      -0.360       0.410
C(countyfips)[T.47011]                 0.1041      0.197      0.530      0.596      -0.281       0.489
C(countyfips)[T.47037]                 0.0587      0.196      0.299      0.765      -0.326       0.444
C(countyfips)[T.47043]                -0.0573      0.196     -0.292      0.770      -0.442       0.328
C(countyfips)[T.47065]                -0.0600      0.197     -0.305      0.761      -0.446       0.326
C(countyfips)[T.47093]                 0.0129      0.196      0.066      0.948      -0.371       0.397
C(countyfips)[T.47113]                 0.0550      0.197      0.279      0.780      -0.331       0.441
C(countyfips)[T.47141]                 0.1354      0.197      0.688      0.492      -0.251       0.522
C(countyfips)[T.47149]                -0.2137      0.197     -1.087      0.277      -0.599       0.172
C(countyfips)[T.47155]                -0.0352      0.201     -0.175      0.861      -0.430       0.360
C(countyfips)[T.47157]                -0.0486      0.196     -0.248      0.804      -0.434       0.336
C(countyfips)[T.47163]                -0.0237      0.196     -0.121      0.904      -0.408       0.360
C(countyfips)[T.47165]                 0.0980      0.197      0.498      0.619      -0.288       0.484
C(countyfips)[T.47179]                 0.0491      0.198      0.248      0.804      -0.338       0.437
C(countyfips)[T.47187]                 0.1185      0.197      0.603      0.547      -0.267       0.504
C(countyfips)[T.47189]                 0.2569      0.196      1.308      0.191      -0.128       0.642
C(countyfips)[T.48013]                -0.0053      0.198     -0.027      0.978      -0.393       0.382
C(countyfips)[T.48021]                 0.0011      0.197      0.006      0.996      -0.384       0.387
C(countyfips)[T.48027]                 0.0086      0.196      0.044      0.965      -0.376       0.393
C(countyfips)[T.48029]                 0.1567      0.196      0.800      0.424      -0.227       0.541
C(countyfips)[T.48039]                -0.1310      0.196     -0.668      0.504      -0.515       0.253
C(countyfips)[T.48041]                -0.0553      0.197     -0.281      0.779      -0.442       0.331
C(countyfips)[T.48061]                -0.0538      0.197     -0.274      0.784      -0.439       0.331
C(countyfips)[T.48085]                 0.1363      0.196      0.695      0.487      -0.248       0.521
C(countyfips)[T.48091]                -0.1117      0.196     -0.569      0.569      -0.496       0.273
C(countyfips)[T.48113]                 0.1137      0.196      0.580      0.562      -0.271       0.498
C(countyfips)[T.48121]                 0.0739      0.196      0.376      0.707      -0.311       0.459
C(countyfips)[T.48139]                -0.1482      0.198     -0.749      0.454      -0.536       0.240
C(countyfips)[T.48141]                -0.1784      0.197     -0.906      0.365      -0.564       0.208
C(countyfips)[T.48157]                -0.0294      0.196     -0.150      0.881      -0.414       0.355
C(countyfips)[T.48167]                -0.2086      0.196     -1.065      0.287      -0.593       0.175
C(countyfips)[T.48171]                -0.0603      0.196     -0.307      0.759      -0.445       0.325
C(countyfips)[T.48181]                -0.0191      0.196     -0.097      0.922      -0.403       0.365
C(countyfips)[T.48183]                 0.1267      0.196      0.646      0.518      -0.258       0.511
C(countyfips)[T.48187]                 0.0169      0.196      0.086      0.931      -0.368       0.402
C(countyfips)[T.48201]                -0.1240      0.196     -0.632      0.528      -0.509       0.261
C(countyfips)[T.48209]                 0.0458      0.196      0.233      0.816      -0.339       0.431
C(countyfips)[T.48215]                -0.0682      0.197     -0.347      0.729      -0.454       0.317
C(countyfips)[T.48221]                -0.2127      0.196     -1.086      0.278      -0.597       0.171
C(countyfips)[T.48231]                -0.1858      0.199     -0.932      0.351      -0.576       0.205
C(countyfips)[T.48245]                -0.2459      0.196     -1.255      0.210      -0.630       0.138
C(countyfips)[T.48251]                 0.1289      0.196      0.656      0.512      -0.256       0.514
C(countyfips)[T.48257]                -0.0091      0.196     -0.046      0.963      -0.394       0.376
C(countyfips)[T.48265]                 0.0888      0.196      0.452      0.651      -0.296       0.473
C(countyfips)[T.48291]                 0.0641      0.197      0.326      0.745      -0.322       0.450
C(countyfips)[T.48303]                -0.0720      0.197     -0.366      0.714      -0.458       0.314
C(countyfips)[T.48309]                 0.0519      0.197      0.264      0.792      -0.333       0.437
C(countyfips)[T.48329]                 0.1592      0.197      0.809      0.419      -0.227       0.545
C(countyfips)[T.48339]                 0.0354      0.196      0.180      0.857      -0.349       0.420
C(countyfips)[T.48355]                -0.0450      0.196     -0.230      0.818      -0.429       0.339
C(countyfips)[T.48367]                -0.0874      0.197     -0.445      0.657      -0.473       0.298
C(countyfips)[T.48375]                -0.0284      0.196     -0.145      0.885      -0.413       0.356
C(countyfips)[T.48381]                -0.1265      0.196     -0.645      0.519      -0.511       0.258
C(countyfips)[T.48397]                -0.1447      0.198     -0.732      0.464      -0.532       0.243
C(countyfips)[T.48423]                 0.0017      0.196      0.009      0.993      -0.382       0.386
C(countyfips)[T.48439]                -0.0734      0.196     -0.374      0.708      -0.458       0.311
C(countyfips)[T.48451]                 0.0237      0.196      0.121      0.904      -0.360       0.407
C(countyfips)[T.48453]                 0.0032      0.196      0.016      0.987      -0.382       0.388
C(countyfips)[T.48469]                 0.1522      0.197      0.773      0.439      -0.234       0.538
C(countyfips)[T.48471]                -0.0633      0.196     -0.323      0.747      -0.448       0.321
C(countyfips)[T.48479]                -0.0591      0.196     -0.301      0.764      -0.444       0.326
C(countyfips)[T.48485]                 0.0815      0.196      0.415      0.678      -0.304       0.467
C(countyfips)[T.48491]                 0.0122      0.196      0.062      0.950      -0.372       0.396
C(countyfips)[T.49005]                 0.0093      0.197      0.047      0.962      -0.377       0.396
C(countyfips)[T.49035]                 0.0706      0.196      0.360      0.719      -0.314       0.455
C(countyfips)[T.49043]                -0.0590      0.197     -0.300      0.765      -0.445       0.327
C(countyfips)[T.49045]                 0.0337      0.197      0.171      0.864      -0.353       0.420
C(countyfips)[T.49049]                -0.0048      0.196     -0.024      0.981      -0.389       0.379
C(countyfips)[T.49057]                 0.0460      0.197      0.234      0.815      -0.339       0.431
C(countyfips)[T.50021]                -0.0529      0.200     -0.265      0.791      -0.444       0.339
C(countyfips)[T.50025]                -0.0390      0.197     -0.198      0.843      -0.424       0.346
C(countyfips)[T.51003]                -0.0021      0.197     -0.010      0.992      -0.387       0.383
C(countyfips)[T.51013]                 0.0326      0.196      0.166      0.868      -0.353       0.418
C(countyfips)[T.51015]                -0.0832      0.197     -0.423      0.672      -0.469       0.302
C(countyfips)[T.51019]                -0.1503      0.199     -0.756      0.450      -0.540       0.240
C(countyfips)[T.51041]                 0.0088      0.196      0.045      0.964      -0.376       0.394
C(countyfips)[T.51047]                -0.1354      0.203     -0.666      0.505      -0.534       0.263
C(countyfips)[T.51059]                -0.2293      0.196     -1.170      0.242      -0.613       0.155
C(countyfips)[T.51061]                -0.0236      0.197     -0.120      0.904      -0.409       0.362
C(countyfips)[T.51069]                 0.0746      0.196      0.381      0.703      -0.309       0.459
C(countyfips)[T.51085]                 0.0568      0.196      0.289      0.773      -0.328       0.442
C(countyfips)[T.51087]                -0.0397      0.196     -0.203      0.840      -0.424       0.345
C(countyfips)[T.51095]                -0.0649      0.197     -0.329      0.742      -0.452       0.322
C(countyfips)[T.51107]                -0.0253      0.196     -0.129      0.897      -0.410       0.359
C(countyfips)[T.51121]                -0.0677      0.198     -0.342      0.732      -0.456       0.321
C(countyfips)[T.51153]                -0.2434      0.196     -1.239      0.215      -0.628       0.142
C(countyfips)[T.51161]                -0.1740      0.199     -0.874      0.382      -0.564       0.216
C(countyfips)[T.51177]                -0.0285      0.197     -0.145      0.885      -0.416       0.358
C(countyfips)[T.51179]                -0.1850      0.199     -0.930      0.352      -0.575       0.205
C(countyfips)[T.51199]                -0.2057      0.200     -1.026      0.305      -0.599       0.187
C(countyfips)[T.51510]                -0.0805      0.196     -0.410      0.682      -0.465       0.304
C(countyfips)[T.51550]                -0.1182      0.196     -0.602      0.547      -0.503       0.267
C(countyfips)[T.51630]                -0.0952      0.196     -0.485      0.627      -0.480       0.289
C(countyfips)[T.51650]                -0.2005      0.197     -1.016      0.310      -0.587       0.186
C(countyfips)[T.51683]                 0.0252      0.197      0.128      0.898      -0.361       0.412
C(countyfips)[T.51700]                -0.2088      0.197     -1.062      0.288      -0.594       0.177
C(countyfips)[T.51710]                 0.0583      0.196      0.297      0.767      -0.327       0.443
C(countyfips)[T.51740]                -0.2863      0.198     -1.446      0.148      -0.674       0.102
C(countyfips)[T.51800]                 0.0440      0.197      0.223      0.823      -0.343       0.431
C(countyfips)[T.51810]                -0.2609      0.196     -1.330      0.184      -0.646       0.124
C(countyfips)[T.51840]                -0.0383      0.197     -0.195      0.846      -0.424       0.347
C(countyfips)[T.53005]                 0.0838      0.196      0.428      0.669      -0.300       0.468
C(countyfips)[T.53007]                -0.0259      0.196     -0.132      0.895      -0.411       0.359
C(countyfips)[T.53015]                 0.0377      0.198      0.191      0.849      -0.350       0.425
C(countyfips)[T.53025]                 0.0442      0.197      0.224      0.823      -0.342       0.431
C(countyfips)[T.53033]                -0.0480      0.196     -0.244      0.807      -0.433       0.337
C(countyfips)[T.53035]                 0.2153      0.196      1.098      0.272      -0.169       0.600
C(countyfips)[T.53041]                -0.0314      0.197     -0.160      0.873      -0.417       0.354
C(countyfips)[T.53053]                -0.0123      0.196     -0.063      0.950      -0.397       0.372
C(countyfips)[T.53057]                -0.1287      0.197     -0.654      0.513      -0.514       0.257
C(countyfips)[T.53061]                -0.0045      0.197     -0.023      0.982      -0.390       0.381
C(countyfips)[T.53063]                 0.0848      0.196      0.433      0.665      -0.299       0.469
C(countyfips)[T.53067]                -0.0045      0.197     -0.023      0.982      -0.390       0.381
C(countyfips)[T.53073]                 0.0296      0.197      0.150      0.880      -0.356       0.415
C(countyfips)[T.54003]                -0.0898      0.196     -0.458      0.647      -0.474       0.295
C(countyfips)[T.54011]                -0.0958      0.197     -0.485      0.628      -0.483       0.291
C(countyfips)[T.54039]                -0.1802      0.196     -0.920      0.358      -0.564       0.204
C(countyfips)[T.54061]                 0.0009      0.196      0.004      0.996      -0.384       0.386
C(countyfips)[T.55009]                 0.0002      0.196      0.001      0.999      -0.384       0.385
C(countyfips)[T.55021]                -0.0670      0.197     -0.340      0.734      -0.453       0.319
C(countyfips)[T.55025]                -0.0760      0.196     -0.387      0.699      -0.461       0.309
C(countyfips)[T.55031]                -0.0761      0.199     -0.382      0.703      -0.467       0.315
C(countyfips)[T.55035]                 0.0145      0.197      0.074      0.941      -0.371       0.400
C(countyfips)[T.55039]                -0.0097      0.197     -0.049      0.961      -0.395       0.376
C(countyfips)[T.55059]                -0.0455      0.196     -0.232      0.817      -0.430       0.339
C(countyfips)[T.55063]                -0.1445      0.200     -0.722      0.470      -0.537       0.248
C(countyfips)[T.55073]                -0.0102      0.197     -0.052      0.959      -0.396       0.375
C(countyfips)[T.55079]                -0.1116      0.196     -0.568      0.570      -0.497       0.273
C(countyfips)[T.55087]                 0.0374      0.197      0.190      0.849      -0.348       0.423
C(countyfips)[T.55089]                 0.0029      0.196      0.015      0.988      -0.382       0.388
C(countyfips)[T.55095]                 0.0412      0.197      0.210      0.834      -0.344       0.426
C(countyfips)[T.55097]                 0.0899      0.196      0.458      0.647      -0.295       0.475
C(countyfips)[T.55101]                -0.0649      0.196     -0.330      0.741      -0.450       0.320
C(countyfips)[T.55111]                -0.0015      0.197     -0.007      0.994      -0.388       0.385
C(countyfips)[T.55117]                -0.0487      0.198     -0.246      0.806      -0.437       0.340
C(countyfips)[T.55127]                -0.0337      0.197     -0.171      0.864      -0.420       0.352
C(countyfips)[T.55131]                 0.0478      0.196      0.244      0.807      -0.336       0.432
C(countyfips)[T.55133]                -0.0029      0.196     -0.015      0.988      -0.388       0.382
C(countyfips)[T.55139]                -0.0441      0.196     -0.225      0.822      -0.428       0.340
C(countyfips)[T.56021]                -0.0259      0.197     -0.131      0.895      -0.413       0.361
C(countyfips)[T.56025]                -0.0633      0.197     -0.321      0.748      -0.449       0.323
l1_spend_all_resid                     0.0102      0.008      1.242      0.214      -0.006       0.026
l1_gps_retail_and_recreation_resid     0.0094      0.011      0.878      0.380      -0.012       0.030
l1_emp_resid                           0.0283      0.011      2.653      0.008       0.007       0.049
l1_revenue_all_resid                   0.0058      0.003      1.775      0.076      -0.001       0.012
==============================================================================
Omnibus:                      330.936   Durbin-Watson:                   1.876
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              995.255
Skew:                          -0.131   Prob(JB):                    7.64e-217
Kurtosis:                       4.726   Cond. No.                     2.16e+03
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.16e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

Unfortunately, this model performs a bit worse than using the raw economic variables. The coefficients are less significant and the fit is overall worse.

The next model I test removes the county fixed-effects, as many of these were insignificant in the fixed-effects model.

In [68]:
# Model without county or time fixed-effects
formula = 'net_flow_std ~ l1_spend_all + l1_gps_retail_and_recreation + l1_emp + l1_revenue_all'

model_num = model_num + 1
ols_model2 = smf.ols(formula, data=long_data_train).fit()
model_stats = add_model_stats(long_data_test, ols_model2, model_num)
print(ols_model2.summary())
                            OLS Regression Results                            
==============================================================================
Dep. Variable:           net_flow_std   R-squared:                       0.027
Model:                            OLS   Adj. R-squared:                  0.026
Method:                 Least Squares   F-statistic:                     84.91
Date:                Sat, 17 Dec 2022   Prob (F-statistic):           2.90e-71
Time:                        20:05:42   Log-Likelihood:                -8365.0
No. Observations:               12406   AIC:                         1.674e+04
Df Residuals:                   12401   BIC:                         1.678e+04
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
Intercept                        0.0043      0.004      0.963      0.335      -0.004       0.013
l1_spend_all                    -0.0787      0.006    -14.269      0.000      -0.089      -0.068
l1_gps_retail_and_recreation    -0.0225      0.006     -3.907      0.000      -0.034      -0.011
l1_emp                           0.0157      0.006      2.795      0.005       0.005       0.027
l1_revenue_all                   0.0167      0.005      3.604      0.000       0.008       0.026
==============================================================================
Omnibus:                      496.388   Durbin-Watson:                   1.887
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1548.882
Skew:                          -0.069   Prob(JB):                         0.00
Kurtosis:                       4.725   Cond. No.                         2.61
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

This model performs better than the prior 2 models, with a larger F-stat and Adjusted R-squared. Additionally, the coefficients on all of the economic variables are significant at the 1% level.

Next, I again try the residuals without the county fixed-effects:

In [69]:
# Model without county or time fixed-effects
formula_resid = 'net_flow_std ~ l1_spend_all_resid + l1_gps_retail_and_recreation_resid + l1_emp_resid + l1_revenue_all_resid'

model_num = model_num + 1
ols_model2_resid = smf.ols(formula_resid, data=long_data_train).fit()
model_stats = add_model_stats(long_data_test, ols_model2_resid, model_num)
print(ols_model2_resid.summary())
                            OLS Regression Results                            
==============================================================================
Dep. Variable:           net_flow_std   R-squared:                       0.001
Model:                            OLS   Adj. R-squared:                  0.001
Method:                 Least Squares   F-statistic:                     2.226
Date:                Sat, 17 Dec 2022   Prob (F-statistic):             0.0636
Time:                        20:05:42   Log-Likelihood:                -5171.0
No. Observations:                7836   AIC:                         1.035e+04
Df Residuals:                    7831   BIC:                         1.039e+04
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
======================================================================================================
                                         coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------------
Intercept                             -0.0229      0.009     -2.683      0.007      -0.040      -0.006
l1_spend_all_resid                     0.0028      0.005      0.505      0.613      -0.008       0.013
l1_gps_retail_and_recreation_resid     0.0082      0.007      1.219      0.223      -0.005       0.021
l1_emp_resid                           0.0105      0.006      1.736      0.083      -0.001       0.022
l1_revenue_all_resid                   0.0021      0.002      1.186      0.236      -0.001       0.006
==============================================================================
Omnibus:                      364.262   Durbin-Watson:                   1.814
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1031.562
Skew:                          -0.208   Prob(JB):                    9.98e-225
Kurtosis:                       4.728   Cond. No.                         6.09
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

In this model, the employment residual is significant at the 10% level, but the other coefficients are insignificant. The model is overall worse than the prior model.

As a final test, I try adding the employment residual to our current top-performing model to see if this improves it at all:

In [70]:
# Model without county or time fixed-effects
formula_mixed = 'net_flow_std ~ l1_spend_all + l1_gps_retail_and_recreation + l1_emp + l1_revenue_all + l1_emp_resid'

model_num = model_num + 1
ols_model_mixed = smf.ols(formula_mixed, data=long_data_train).fit()
model_stats = add_model_stats(long_data_test, ols_model_mixed, model_num)
print(ols_model_mixed.summary())
                            OLS Regression Results                            
==============================================================================
Dep. Variable:           net_flow_std   R-squared:                       0.021
Model:                            OLS   Adj. R-squared:                  0.020
Method:                 Least Squares   F-statistic:                     33.52
Date:                Sat, 17 Dec 2022   Prob (F-statistic):           5.56e-34
Time:                        20:05:42   Log-Likelihood:                -5092.4
No. Observations:                7836   AIC:                         1.020e+04
Df Residuals:                    7830   BIC:                         1.024e+04
Df Model:                           5                                         
Covariance Type:            nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
Intercept                       -0.0084      0.006     -1.310      0.190      -0.021       0.004
l1_spend_all                    -0.0669      0.009     -7.259      0.000      -0.085      -0.049
l1_gps_retail_and_recreation    -0.0520      0.008     -6.878      0.000      -0.067      -0.037
l1_emp                           0.0110      0.010      1.088      0.276      -0.009       0.031
l1_revenue_all                   0.0072      0.008      0.921      0.357      -0.008       0.023
l1_emp_resid                     0.0106      0.006      1.681      0.093      -0.002       0.023
==============================================================================
Omnibus:                      332.170   Durbin-Watson:                   1.854
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              924.726
Skew:                          -0.178   Prob(JB):                    1.58e-201
Kurtosis:                       4.645   Cond. No.                         2.78
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

While the employment residual is significant at the 10% level, the lagged employment and revenue variables become insignificant and the model overall has poorer fit than when excluding the residuals. This is likely because residuals are noisy, and in this case that noise does not seem to strongly correlate with the noise of the migration flows.

The diagnostics are summed in this table:

In [71]:
print(model_stats)
         r2    adj_r2     f_stat      f_stat_p   RMSE
1  0.035519 -0.018332   0.659579  1.000000e+00  0.459
2  0.040901 -0.046739   0.466689  1.000000e+00  0.496
3  0.026657  0.026343  84.908008  2.901029e-71  0.452
4  0.001136  0.000626   2.226429  6.360168e-02  0.454
5  0.020957  0.020331  33.520490  5.559459e-34  0.453

Summary: The best model across the diagnostics is the model with the lagged economic variables and no county fixed-effects. This model has the largest F-stat and adjusted R-squared and the lowest RMSE, making it the preferred specification, though it is still not a very good model in terms of fit. Since none of the models are performing very well, I will also test a version of the county fixed-effect model after applying regularization.

Finally, let's check the residuals of the preferred model:

In [73]:
long_data_test = compute_residuals(long_data_test, ols_model2)
plot_resid_dist(long_data_test)
residual_plot(long_data_test)
print('\nThe STD of the residuals = {}'.format(np.round(np.std(long_data_test['resids']), 3)))
The STD of the residuals = 0.452

The standard deviation of the residuals is large, which is also clear from the residuals plots. The residuals also skew right and are therefore not normally distributed. This is expected given the low R-squared of the model, suggesting that the model does not fit the data very well. The residuals look roughly homoskedastic, though the variation is a bit greater in the middle of the plot.

As a robustness check, I also test the model using a Huber estimator.

In [74]:
formula = 'net_flow_std ~ l1_spend_all + l1_gps_retail_and_recreation + l1_emp + l1_revenue_all'

ols_model_huber = smf.rlm(formula, data=long_data_train, M=sm.robust.norms.HuberT()).fit()
print(ols_model_huber.summary())
                    Robust linear Model Regression Results                    
==============================================================================
Dep. Variable:           net_flow_std   No. Observations:                12406
Model:                            RLM   Df Residuals:                    12401
Method:                          IRLS   Df Model:                            4
Norm:                          HuberT                                         
Scale Est.:                       mad                                         
Cov Type:                          H1                                         
Date:                Sat, 17 Dec 2022                                         
Time:                        20:07:58                                         
No. Iterations:                    19                                         
================================================================================================
                                   coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------------------------
Intercept                        0.0067      0.004      1.646      0.100      -0.001       0.015
l1_spend_all                    -0.0708      0.005    -13.874      0.000      -0.081      -0.061
l1_gps_retail_and_recreation    -0.0158      0.005     -2.951      0.003      -0.026      -0.005
l1_emp                           0.0096      0.005      1.837      0.066      -0.001       0.020
l1_revenue_all                   0.0171      0.004      3.988      0.000       0.009       0.026
================================================================================================

If the model instance has been used for another fit with different fit parameters, then the fit options might not be the correct ones anymore .
In [76]:
long_data_test = compute_residuals(long_data_test, ols_model_huber)
plot_resid_dist(long_data_test)
residual_plot(long_data_test)
print('\nThe STD of the residuals = {}'.format(np.round(np.std(long_data_test['resids']), 3)))
The STD of the residuals = 0.452

Using the Huber model shows little improvement in estimating the residuals. This is due to the coefficients being very similar between the OLS and the Huber models, which means the OLS model is robust to accounting for outliers. The main difference is that the employment variable loses significance, but it is still significant at the 10% level. I will therefore proceed with the original OLS model as the preferred specification.

Applying Regularization to the Models¶

In this section, I apply a mix of L1 and L2 regularization to the county fixed-effect model in an attempt to improve the accuracy of the model. First, I define some functions to handle the regularization:

In [78]:
# Functions are from Stephen Elston's Lesson 10 Notebook
def regularized_coefs(df_train, df_test, alphas, L1_wt=0.0, n_coefs=8,
                      formula = formula, label='net_flow_std'):
    '''Function that computes a linear model for each value of the regualarization 
    parameter alpha and returns an array of the coefficient values. The L1_wt 
    determines the trade-off between L1 and L2 regualarization'''
    coefs = np.zeros((len(alphas),n_coefs + 1))
    MSE_train = []
    MSE_test = []
    for i,alpha in enumerate(alphas):
        ## First compute the training MSE
        #### Complete the line of code below
        temp_mod = smf.ols(formula, data=df_train).fit_regularized(alpha=alpha,L1_wt=L1_wt)
        
        ## Save the coefficient values   
        coefs[i,:] = temp_mod.params
        ## Compute and save the training RMSE
        MSE_train.append(sqrt(np.mean(np.square(df_train[label] - temp_mod.predict(df_train)))))
        ## Then compute the test RMSE
        MSE_test.append(sqrt(np.mean(np.square(df_test[label] - temp_mod.predict(df_test)))))
        
    return coefs, MSE_train, MSE_test


def plot_coefs(coefs, alphas, MSE_train, MSE_test, ylim=None, \
               title='MSE vs. regularization parameter number',\
               ylab='Root mean squared error', location='lower right'):
    fig, ax = plt.subplots(1,2, figsize=(12, 5)) # define axis
    for i in range(coefs.shape[1]): # Iterate over coefficients
        ax[0].plot(alphas, coefs[:,i])
    ax[0].axhline(0.0, color='red', linestyle='--', linewidth=0.5)
    ax[0].set_ylabel('Partial slope values')
    ax[0].set_xlabel('alpha')
    ax[0].set_title('Parial slopes vs. regularization parameter')
    if ylim is not None: ax[0].set_ylim(ylim)
    
    ax[1].plot(alphas, MSE_train, label='Training error')
    ax[1].plot(alphas, MSE_test, label='Test error')
    ax[1].set_ylabel(ylab)
    ax[1].set_xlabel('alpha')
    ax[1].set_title(title)
    plt.legend(loc=location)
    plt.show()

np.random.seed(12856)

I use these functions to test the model with the county fixed-effects. The point of testing this model is to see if any of the county fixed-effects survive regularization. There's a chance that a few of the county variables do matter, in which case they should be included in the model. For this, I also use an L1 weight of 0.5.

In [81]:
formula_fe = 'net_flow_std ~  l1_spend_all + l1_gps_retail_and_recreation + l1_emp + l1_revenue_all + C(countyfips)'
alphas = np.arange(0.0, 0.001, step = 0.0001)
Betas, MSE_train, MSE_test = regularized_coefs(long_data_train, long_data_test, alphas, n_coefs=656, formula=formula_fe, L1_wt=0.5)

plot_coefs(Betas, alphas, MSE_train, MSE_test)

The regularization reduces most of the coefficients to 0, while a few stay consistent throughout. The test error plateaus at an alpha of about 0.0004, so I use this value to estimate the new coefficients.

To get a sense of how the coefficients in this model compare to the original model, I display the following statistics:

In [82]:
elastic_model = smf.ols(formula_fe, data=long_data_train).fit_regularized(alpha=0.0004, L1_wt=0.5)

print_coefficient_comparision(elastic_model, ols_model_fe)
print('\n')
print_metrics(long_data_test, elastic_model)   
long_data_test = compute_residuals(long_data_test, elastic_model)
plot_resid_dist(long_data_test)
residual_plot(long_data_test)
                              Compare model     Model
Intercept                         -0.028487  0.004224
C(countyfips)[T.1055]             -0.063334  0.000000
C(countyfips)[T.1069]              0.062729  0.000000
C(countyfips)[T.1073]             -0.098584  0.000000
C(countyfips)[T.1081]              0.065888  0.000000
...                                     ...       ...
C(countyfips)[T.56025]            -0.030234  0.000000
l1_spend_all                      -0.079725 -0.078352
l1_gps_retail_and_recreation      -0.024235 -0.022101
l1_emp                             0.018944  0.015185
l1_revenue_all                     0.016772  0.016433

[657 rows x 2 columns]

Magnitude of base model = 1.43  Without intercept = 1.43
Magnitude of new model = 0.09  Without intercept = 0.09


MSE  =  0.214
RMSE =  0.463
MAE  =  0.236

We see that the regularization got rid of most of the county fixed-effects, but kept all of the economic variables. This makes the model basically the same as using the model without the county fixed-effects, showing that including these in the model specification did not improve the results. My preferred model, therefore, remains the OLS model with the lagged economic variables and no county fixed-effects.

I finally test the correlations between the coefficients of the preferred model to get a sense of any multicollinearity that may arise:

In [86]:
formula = 'net_flow_std ~ l1_spend_all + l1_gps_retail_and_recreation + l1_emp + l1_revenue_all'
## Compute correlation matrix 
y, design_matrix = patsy.dmatrices(formula, data=long_data_train)
corr_mat = np.corrcoef(np.transpose(design_matrix))

## Display correlation matrix  
c_names = list(design_matrix.design_info.column_name_indexes)
fig,ax = plt.subplots(figsize=(10,8))
sns.heatmap(corr_mat, xticklabels=c_names, yticklabels=c_names, ax=ax);
C:\Users\nloreedwards\Anaconda3\lib\site-packages\numpy\lib\function_base.py:2691: RuntimeWarning:

invalid value encountered in true_divide

C:\Users\nloreedwards\Anaconda3\lib\site-packages\numpy\lib\function_base.py:2692: RuntimeWarning:

invalid value encountered in true_divide

This figure shows that the model coefficients are somewhat correlated, though none of them have a correlation above about 0.7, and many appear to have weak positive correlations. This is good to check, since the economic variables may measure similar attributes of the county. Based on this figure and the significant coefficients in the regression, this does not appear to be a problem.

Plotting the predicted timeseries¶

Finally, I can now use the preferred model to estimate the residuals of the timeseries in the testing data. I plot the predicted residuals for 6 counties, in addition to the actual residuals. Given the diagnositc statistics I've presented throughout, I do not expect a good fit, though the hope is that this is a slight improvement over using a random residual value.

In [83]:
# Compute residuals using preferred model
long_data_test = compute_residuals(long_data_test, ols_model2)

fig, ax = plt.subplots(3,2, figsize=(16,16))
ax = ax.flatten()
for i, cty in enumerate([1003, 28033, 48167, 36101, 13135, 4013]):
    ax[i] = sns.lineplot(data= long_data_train[long_data_train['countyfips'] == cty], x='time', y='net_flow_std', ax=ax[i])
    ax[i] = sns.lineplot(data= long_data_test[long_data_test['countyfips'] == cty], x='time', y='predicted', ax=ax[i])
    ax[i] = sns.lineplot(data= long_data_test[long_data_test['countyfips'] == cty], x='time', y='net_flow_std', ax=ax[i])
    ax[i].set_ylabel('Net Flow rel Population (residuals)')
    ax[i].set_xlabel("Year-Month")
    ax[i].set_title("County FIPS: " + str(cty))
    ax[i].legend(['Training', 'Predicted', 'Observed'])
    
plt.show()

The plots of the residuals and the predicted residuals show that the predicted residuals are very small and do not have much variation. This is due to the small coefficients on the OLS regression. That being said, they tend to at least be in the range of the actual values, and are likley better than using random residuals.

Now that I have a predcited value for the residuals, I can add back in the seasonal trends and compare the detrended predicted and actual values.

In [84]:
# Calculate variables with seasonal components
long_data_train['net_flow_detrended'] = long_data_train['net_flow_std'] + long_data_train['seasonal_adjustment']
long_data_test['net_flow_detrended'] = long_data_test['net_flow_std'] + long_data_test['seasonal_adjustment']
long_data_test['predicted_detrended'] = long_data_test['predicted'] + long_data_test['seasonal_adjustment']

fig, ax = plt.subplots(3,2, figsize=(16,16))
ax = ax.flatten()
for i, cty in enumerate([1003, 28033, 48167, 36101, 13135, 4013]):
    ax[i] = sns.lineplot(data= long_data_train[long_data_train['countyfips'] == cty], x='time', y='net_flow_detrended', ax=ax[i])
    ax[i] = sns.lineplot(data= long_data_test[long_data_test['countyfips'] == cty], x='time', y='predicted_detrended', ax=ax[i])
    ax[i] = sns.lineplot(data= long_data_test[long_data_test['countyfips'] == cty], x='time', y='net_flow_detrended', ax=ax[i])
    ax[i].set_ylabel('Net Flow rel Population (detrended)')
    ax[i].set_xlabel("Year-Month")
    ax[i].set_title("County FIPS: " + str(cty))
    ax[i].legend(['Training', 'Predicted', 'Observed'])
    
plt.show()

The detrended results look much better, as the seasonal variation provides a good estimate of the net flows behavior. While the predicted residuals were not very accurate, the accuracy of the seasonal trends makes this version fit the data much better. Finally, I add back in the trend data and look at how this affects the results.

In [85]:
# Calculate variables with seasonal and trend components
long_data_train['net_flow_trended'] = long_data_train['net_flow_std'] + long_data_train['seasonal_adjustment'] + long_data_train['trend_adjustment']
long_data_test['net_flow_trended'] = long_data_test['net_flow_std'] + long_data_test['seasonal_adjustment'] + long_data_test['trend_adjustment']
long_data_test['predicted_trended'] = long_data_test['predicted'] + long_data_test['seasonal_adjustment'] + long_data_test['trend_adjustment']

fig, ax = plt.subplots(3,2, figsize=(16,16))
ax = ax.flatten()
for i, cty in enumerate([1003, 28033, 48167, 36101, 13135, 4013]):
    ax[i] = sns.lineplot(data= long_data_train[long_data_train['countyfips'] == cty], x='time', y='net_flow_trended', ax=ax[i])
    ax[i] = sns.lineplot(data= long_data_test[long_data_test['countyfips'] == cty], x='time', y='predicted_trended', ax=ax[i])
    ax[i] = sns.lineplot(data= long_data_test[long_data_test['countyfips'] == cty], x='time', y='net_flow_trended', ax=ax[i])
    ax[i].set_ylabel('Net Flow rel Population (std.)')
    ax[i].set_xlabel("Year-Month")
    ax[i].set_title("County FIPS: " + str(cty))
    ax[i].legend(['Training', 'Predicted', 'Observed'])
    
plt.show()

Adding in the trend data shows that the primary improvement in estimation came from the seasonal adjustment, as the data follows a strongly seasonal pattern.

Overall, the full model follows actual migration patterns pretty closely, though this is largely due to the seasonal component of the data. Adding in the economic variables to predict the residuals did not offer much improvement, despite strong correlations between the raw values of these variables and migration patterns.

Conclusion¶

This project sought to understand the relationship, if any, between economic indicators being collecting during the COVID-19 pandemic and migration patterns, as measured by USPS address changes. Through data exploration, I found that migration flows have highly seasonal behavior, as do some (but not all) economic indicators. Furthermore, the correlation between the economic variables and migration varies by county and time, making it difficult to generalize the correlation of one with another. Through an OLS model with county and month fixed-effects, I find that credit/debit card spending, employment, and small business revenue are all negatively correlated with migration to a county, on average, significant at the 1% level. On the other hand, traffic to retail and recreation businesses is positively correlated with migration, on average, also significant at the 1% level.

These significant correlations raise the question of whether economic variables can be used to increase the accuracy of predicting migration patterns at the county-level. I find that incorporating economic variables into predicting migration patterns only results in modest gains in accuracy in the short-term. Simply using the seasonal variation of migration patterns at the county-level is enough to closely predict future migration trends. Given the limited availability of the economic variables relative to the migration data, simply exploiting the seasonal and trend variation of past migration patterns is likely to best way to predict future trends.